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E.LSchatzman 

The Structure 
of the Universe 



World 

University 

Library 




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It is over forty years now since it became 
known that our system of stars, of which 
the sun is a member, is only one of many 
such systems or galaxies. These galaxies, 
each made up of vast numbers of suns, are 
racing away from each other ; the whole 
universe seems to be expanding. And during 
the last few years, astronomers have 
identified the strange, super-luminous 
objects known as quasars - so far away that 
their light now reaching us started on its 
journey before the Earth came into 
existence. 

Yet despite this remarkable increase in our 
knowledge, how much is really known 
about the history of the galaxies and the 
structure of the universe in general ? 
Is 'space' limited, or is it infinite 1 How old 
is the universe, and how long may it be 
expected to endure ? These and other 
questions are discussed by Professor 
Schatzman in the light of the latest findings 
of astronomy and astrophysics. 

With 6 colour and 17 black and white 
photographs and S3 diagrams 



The jacket shows the Horse's Head Nebula. 
NGC 2024 in Orion. 

Photographed with a 48 inch Schmidt telescope 
,it Palomar. 



Price {in UK only) 

30s net 



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World University Library 

The World University Library is an international scries 
of books, each of which has been specially commissioned. 
The authors are leading scientists and scholars from all over 
the world who. in an age of increasing specialisation, sec the 
need for a broad, up-to-date presentation of their subject. 
The aim is to provide authoritative introductory books for 
university students which will be of interest also to the general 
reader. The series is published in Britain, France, Germany, 
Holland, Italy, Spain, Sweden and the United States. 



E. L. Schatzman 



The Structure of the 
Universe 

translated from the French by Patrick Moore 



World University Library 



Weidenfeld and Nicolson 
5 Winsley Street London W1 



78 2 



, 



© E. L. Schat2man 1968 

Translation © George Weidenfeld and Nicolson Ltd 1968 
Phoiotypeset by BAS Printers Limited, Wallop, Hampshire 
Primed by Offlcine Grafichc Arnoldo Mondadori. Verona 



Contents 



1 Introduction 



The Galaxy 

A short description of the universe 

Distance determinations 

Absolute magnitude 

Star-sl reaming 

The Doppler effect 

The distances of the stars in a stream 

Variable stars 

The distribution of stars in the Galaxy 

Gravitation 

Dwarfs and giants 

Gas and dust 

Radio radiation (lines) 

Radio radiation (continuous emission) 

X-rays 

Cosmic rays 

Movements of particles in a magnetic field 

The magnetic field of the Galaxy 

The polarisation of light 

Interstellar polarisation 

Synchrotron radiation 

Faraday rotation 

Radio sources and cosmic radiation 

Conclusion 



9 
23 



Time 

Time in the mechanical sense 

Time and energy 

Time and light 

Time and the atom 

Radioactivity 

Cosmical chronology 

The age of the Earth 

The age of the radioactive elements 

Stellar energy 



85 



Stellar evolution 

The ages of the stars in the Galaxy 

The evolution of the Galaxy 

Nucleosynthesis 

Supernova 

Formation of the heavy elements - the neutron 

Beta -radioactivity and ihe neutrino 

Capture of slow neutrons 

Capture of fast neutrons 

The chemical composition of matter in the Galaxy 

Globular clusters 

Old stars 

Conclusion 

4 Space and the galaxies 

The distances of the neighbouring galaxies 

Highly luminous stars 

Clusters of galaxies 

The red shift 

Classification of galaxies 

Optical appearance 

Spectral classification of galaxies 

Radio sources 

Optical appearances of radio sources 

Radio properties of different optical types 

Multiple galaxies 

VI asses of galaxies 

The mass/luminosity relation 

The formation of spiral galaxies 

Spiral structure 

Elliptical galaxies 

The virial 

Encounters between stars 

Energy of elliptical galaxies 

Clusters of galaxies 

Quasi-stellar radio sources 

Conclusion 



The universe 

The structure of the inner metagalaxy 

More remote regions 

Clusters of galaxies 

The tendency to grouping 

Large clusters 



118 



169 



Statistical methods 

Mean density 

Olbers" paradox 

Radio sources 

Cosmic rays 

Cosmology 

The idea or curvature 

Geometry on a surface 

Geometry in space 

The three proofs of relativity 

Schwarzschild's singularity 

Collapse or explosion ? 

Single galaxies 

The curvature of space 

Newtonian cosmology 

Einstein's cosmology 

Friedman n's cosmology 

Cosmical acceleration 

Cosmic lime 

The cosmic horizon 

Continuous creation 

Comment about time 

The search for proof 

Nature of the red shift 

Cosmological tests 

Quasars 

Matter and anti-matter 

The age* of the stars and the universe 

The diameters of the clusters of galaxies 

Counts of galaxies 

The Singular State, or the Big Bang 

The universe and cosmogony 

Conclusions 



6 Summary 
Bibliography 



Acknowledgments 



Index 



247 



249 



250 



251 



1 Introduction 



During ihe past few centuries, the limits of the known universe 
have been further and further extended. It was Copernicus who 
first revived the ancient idea that the Sun lies in the centre of the 
Solar System, and that the Earth is nothing more than an ordinary 
planet; since the stars do not seem to move appreciably compared 
with each other, it was reasonable to suppose thai they must be 
extremely distant. Copernicus" great book De Revolutionibus 
Orbium Carlestium, published in 1543. caused a complete change in 
the astronomical outlook. Before many more decades had passed, 
the old idea of an Earth-centred universe had been abandoned. 

The first suggestions that there may be star-systems far beyond 
the boundaries of our own system, or Galaxy, were made in the 
1 8th century. In 1 750 Thomas Wright, an English instrument- 
maker who lived from I7ll to 1786. speculated about 'isolated 
systems' in space, though it must be admitted that his ideas were 
decidedly confused and unscientific. Five years later, the German 
philosopher Immanuel Kant put forward a more coherent theory, 
and his ideas were generally accepted for many years. 

Various dim. hazy patches known as nebulae arc to be seen in 
the night sky; of these, the most famous is the Nebula in Andro- 
meda, generally known as Messier 3 1 (M3I) because it was the 
3 1 st object in a later catalogue of nebulae and star-clusters drawn 
up by the French astronomer Charles Messier. Several nebulae 
were listed by M. de Maupertuis as long ago as 1 742. Kant regarded 
them as external systems, far beyond our Milky Way or Galaxy, 
and in this he was of course correct, even though proof could not 
then be obtained. Humboldt, the great explorer and scientist, 
called these systems 'island universes', a term which is still often 
used. 

Throughout the I8th and I9th centuries the nebulae were closely 
studied, and many more were found, notably by Sir William 
Herschcl, possibly the greatest astronomical observer of all time, 
who was inclined to support Kant's 'island universe* theory even 
though he was reluctant to commit himself loo firmly. However, 
the question had to remain open so long as it remained impossible 



1 Circumpolar star-trails (exposure 2 hours 14 minutes). The photograph 
also shows the track ol a meteor which happened to cross the 
field of view during the exposure. The short, bright trail near the 
centre of the picture is the Pole Star. The fact that a trail shows 
demonstrates that Polaris is not exactly at the polar point {though, 
admittedly, its distance from the celestial pole is less than 1 degree) 



11 




lo measure the distances of the nebula. In 1838 F.W.Bessct, in 
Germany, measured the first star-distance, but his method could 
not be applied to much more remote objects, and less direct means 
of investigation were essential. 

The situation changed during the years following 1885. The 
appearance of a nova, or temporary star, in the Andromeda 
Nebula was very significant; it reached naked -eye visibility for a 
brief period in 1885, and is now known to have been a supernova 
that is lo say, a tremendous stellar outburst during which a star 
'explodes' and hurls much of its material away into space. Then 
in 1917 Ritchey, working at the Mount Wilson Observatory with 
the new 100-inch reflecting telescope, discovered a nova in the 
spiral nebula NGC 6946 (that is to say. No. 6946 in the New 
General Catalogue of nebulae drawn up by J.L.E. Dreyer at 
Armagh Observatory). Examination of old photographic plates 
showed two further nova; in the Andromeda Galaxy in 1909. 
These discoveries indicated thai the nebula? were likely to be 
external systems. However, final proof was obtained by E.E. 
Hubble, following a study of the remarkable variable stars known 
as Cepheids. 

Most stars (including our Sun) shine steadily, but there are some 
which fluctuate in brightness over short periods. It was found that 
with the variables, called Cepheids (because the brightest member 
ul the group is the star Delia Cephei), the real luminosity is linked 
with the period of variation; the longer the period, the greater the 
luminosity. Therefore, the distance of a Cepheid may be calculated 
simply by observing its regular changes in brightness. In 1923 
Hubble, again using the Mount Wilson 100-inch reflector, found 
Cepheids in the Andromeda Nebula, and it was at once clear that 
the Nebula could not possibly belong to our Galaxy. Its distance 
had to be measured in hundreds of thousands of light-years - a 
light-year being the distance travelled by a ray of light in one year 
equivalent to almost 6 million million miles. We now know that 
the Andromeda Nebula is over 2,000.000 light-years away. The 
term 'nebula* for these external systems is rapidly becoming 



12 



obsolete, since a true nebula is a gas-cloud in our own Galaxy, and 
the external objects are galaxies in their own right. Many of them, 
including Messier 31, are spiral in shape. 

Another interesting development was that the galaxies were 
found to be receding from us. By spectroscopic methods, to be 
described below, the velocities of recession could be measured, and 
many measurements were made by Hubble and his colleague. M. 
Humason, following 1912. It was found that apart from Messier 31 
and a few other galaxies now known to be members of our local 
group, the galaxies were moving away - and the speeds of recession 
increased for the more distant galaxies. This led on to the so-called 
Hubble-Humason Law, linking recession with distance. By 1938 it 
seemed that a reliable relationship had been found, and this was 
still adopted by Einstein in i950, when he published the third 
edition of his work entitled The Meaning of Relativity. On the 
assumption that the whole universe is expanding, and that the rate 
of expansion has always been constant, it was found that the 
expansion must have begun some 1.800.000,000 years ago, which 
would presumably correspond to the age of the universe. (It is now 
clear thai this figure is a gross underestimate.) The methods which 
Hubble used for this determination are given at the end of the book. 

Between 1952 and 1957 it became obvious that the estimated 
distances of the galaxies, and hence their velocities of recession, 
were much too low. By 1957 the time-scale had been increased 
sevenfold from the value adopted in 1938. The original work was 
due to Walter Baade. working with the 200-inch Palomar reflector 
in California, who announced his results at the 1952 Congress of 
the International Astronomical Union. Baade found that there was 
an error in the Cepheid period-luminosity law - or, more accurately, 
that there are two diftcrent kinds of Cephcids, one type being 
considerably more luminous than the other. The error meant thai 
instead of being a mere 900.000 light-years away, as had been 
thought, the distance of the Andromeda Galaxy must be at least 
1.800,000 light-years, and there would have to be corresponding 
increases for ail the other galaxies, so that the observable universe 



13 



was more than twice as large as had been estimated. Since then, the 
accepted value for the distance of Messier 31 has been further 
increased, this time to 2,200,000 light-years. 

Human nature is often strangely reluctant to recognise facts 
which will lead to major changes in outlook. For instance, the 
French astronomer Henri Mineur. in 1946, had noted the differences 
between the two types of Cepheid variables, but had imagined that 
there must be a serious error in his interpretation, and in his calcula- 
tions he had simply taken an average value for the two types. In 
fact. Mineur had all the essential information in his hands, but had 
been unable to interpret it in the same way that Baade did seven 
years later. 

Baade's results were soon firmly supported by other astronomers, 
and it became clear that Hubble's older methods would have to be 
re-examined with a critical eye to see which of them could be 
retained. In 1956 Humason, Maya II and Sandage. at Palomar. 
announced a revised increase in the distances of the galaxies, 
working this time from a re-calibration of the brilliancies of the 
galaxies themselves. Almost immediately after this, Sandage 
undertook a study of the individual stars in some of the galaxies, 
and yet another distance-increase resulted. However, it seems that 
the estimates arc al last being made on a reliable basis, and it is 
probable that no major errors remain. 

In the early 1930s it was discovered that radio waves can be 
received from space. These are collected by means of radio tele- 
scopes, which come in many designs: they arc quite unlike optical 
telescopes, and do not produce visible pictures of the objects under 
study, but they can provide information which could not be 
collected in any other way, and since the end of the war, radio 
astronomy has become of vital importance. Improvements in 
techniques mean that it is now possible to find the positions of 
radio sources with reasonable accuracy. At an early stage it was 
found that the radio sources do not coincide with bright stars, but 
with objects of different kinds. Supernova remnants in our Galaxy 
emit radio waves, and there are various special galaxies which are 






2 The Coelostat at the solar tower in 
Tokyo Observatory is typical of many 
others in the world. During recent years, 
intensive solar studies have been carried out 
by Japanese astronomers at Tokyo and 
elsewhere. (Photographed in 1966) 



15 




remarkably powerful in the radio range. Mills* catalogue (the 
3-C or third Cambridge catalogue), published in 1 962, lists about 
1.200 sources of all kinds. Since radio telescopes can be made to a 
large size, very weak signals can be picked up, and indeed radio 
telescopes can penetrate further into the universe than optical 
telescopes. 

Another remarkable discovery was made early in the 1960s. Some 
of the radio sources were identified with objects which looked 
optically very much like faint stars, but are now called quasi- 
stellar objects (QSOs) or quasars. If our present interpretations are 
correct, quasars are very remote and super-luminous perhaps 100 
times more luminous titan ordinary galaxies. Much work remains 
to be done, but it docs seem that the distances of some of the 
quasars exceed 6,000 million light-years. 

When we turn to the theories of cosmology, or the past and 
future history of the universe, it is convenient to begin with a book 
entitled Cosmobgische Briefe, published by the German astronomer 
Lambert in 1761. (It is interesting to note, in passing, that the 
French translation appeared in 1770, and was printed in Belgium 
by the clandestine press at Bouillon.) Lambert rejected the idea 
that the Earth lies at the centre of the universe; this, of course, was 
only to be expected. But in addition to this, he suggested that the 
Sun was an ordinary star in our Galaxy, and that the Galaxy itself 
was nothing more than a typical system or island universe, lying 
among other systems of island universes. Some of Lambert's ideas 
are now known to be wrong, but his work was of great importance, 
and it is certainly true that neither the Sun nor our own particular 
Galaxy is of any importance whatsoever in the universe considered 
as a whole. 

Much later, Seeligcr (1895) and Neumann (1896) developed 
cosmological theories, basing their ideas upon Newtonian mechan- 
ics. They had no choice; Einstein's theories, which modified the old 
Newtonian ideas, had not then appeared. But it has become very 
clear that Einsteinian relativity is of prime importance in cosmology, 
and it may be said that the new era opened in 1917, with the 



16 






publication of his Cosmohgkal Considerations. 

The German scientist Mach had suggested that the inertia or a 
body must be determined entirely by the total distribution of mass 
in the universe. Einstein accepted this idea, and found that it could 
be satisfied by a model of the universe consisting of a spherical 
closed system, without, however, introducing any definite 'outer 
edge'. The equations of relativity theory were such that the 
mathematical requirements for such a universe could be satisfied 
Then, in 1917. the Dutch astronomer W.de Sitter found that there 
was a further possibility, not considered by Einstein in his original 
book. De Sitter showed that one direct consequence of the equa- 
tions of general relativity could be an empty but expanding 
universe. The idea of a universe devoid of matter seems at first 
sight, to be quite opposed to the very ideas which had been put 
forward in the new theory of gravitation which Einstein had termed 
general relativity, and it was always clear that the Dc Sitter universe 
cannot correspond to reality, but theoretically it was of great 
significance. Five years later, Friedman n, one of the greatest of 
Russian mathematicians, showed that there are other non-static 
solutions of Einstein's equations and it was Friedmann's results 
which gave the first clear indication of cosmological models 
containing matter in a state of expansion. 

It would be very difficult to describe all the cosmological models 
which have been proposed during the past forty years or so but 
something must be said about the work of Lemaitre and of 
Eddmglon. which were of special importance. In 1927 Canon 
Lemaitre, of Belgium, put forward his theory thai the universe 
began at a set moment in the remote past, and that all the material 
was originally concentrated into what has been termed a 'primaeval 
atom ; subsequently he summarised his theories in a book 
Tiieone <k Atoms PrimMf. In 1930 Sir Arthur Eddinglon of 
Britain, drew attention to Lcmaitre's theories, and made manv 
original contributions of his own. 

There can be no doubt that developments in astronomical theory 
have provided a powerful stimulus to cosmological research, and 



3 The 250 ft paraboloid at the Jodrell Bank Radio Astronomy Observatory in 
Cheshire. This great instrument remains the largest fully-steerable radio telescope 
in operation, and it has been responsible (or fundamental advances in research 
into radio astronomy. It has even been used occasionally for tracking satellites 
and space- probes, though this is certainly not (he purpose for which it was 
designed, and it is not now used in this way. (Photographed in 1 966). 




18 



the two branches of research are closely linked. In 1938. for instance, 
Bethe in America and von Weizsacker in Germany independently 
found that the source of stellar energy is to be found in nuclear 
reactions taking place deep inside the stars; this meant that the 
Galaxy must be several thousands of millions of years old. The 
age of the Earth, too, was estimated more precisely, and by 1946 was 
taken to be at least 3,000 million years (the current estimate is 
4,700 million years). Obviously, this did not fit in with the idea 
that the universe itself was only about 1.800 million years old. and 
in 1948 three astronomers at Cambridge University - H.Bondi, T. 
Gold and F.Hoyle - attempted to solve the discrepancy by means 
of a novel and most interesting theory, in which the universe was 
taken to be in a steady state, with fresh matter being continuously 
created out of nothingness. In their subsequent researches, the 
Cambridge group were led to introduce modifications into general 
relativity theory in order to fit into this steady-state hypothesis. 

The first results of the work of the American astronomer 
Schwarzschild and his pupils in connection with the evolution of 
the stars were discussed at the Rome congress of the International 
Astronomical Union in 1952. This work led to a much more 
accurate determination of the ages of the majority of the stars, and 
further information was gathered steadily, leading to evidence in 
favour of objects perhaps 1 5,000, 20,000 or even 25,000 million 
years old. Here, too, there was an apparent contradiction of the 
same kind as that which had led to the steady-state theory of the 
universe; some of the stars appeared to be much too old to fit in 
with the estimated age of the universe as calculated from the 
present-day expansion rate. Difficulties of this kind serve to place 
even more emphasis upon the close relationship between astronomy 
and cosmology. 

Another aspect of the cosmological problem concerns whal is 
known as the singular state, that is, that time when all the material 
in the universe was concentrated into one very small area of space. 
Conditions of very great density must also involve remarkably high 
temperatures. When temperatures of several thousand million 



4 The72-in Tautenburg reflector. This has a complex optical system 
and can be used either as a conventional reflector, such as a 
Cassegrain, or as a Schmidt, It takes a great deal of lime and work 
to change from one optical system to another in normal telescopes, 
but with the Tautenburg reflector the change from Cassegrain 
to Schmidt, or vice versa, takes only a few hours. 



19 




20 



degrees are reached, an equilibrium is established, which deter- 
mines the relative abundance of the nuclei of the various chemical 
elements, and the first attempts to explain the origin of the elements 
by equilibrium at very high temperature were made by Chand- 
rasekhar and Henrich, but without real success. By the process of 
equilibrium alone, it seemed hopeless to satisfy the conditions 
under which the present-day relative abundances of the elements 
could have been reached. This difficulty led to the development of 
two different theories, each of which seemed to be outwardly 
plausible at the time. In 1950 Alpher, Bethe and Gamow suggested 
that the whole process of element-building, so to speak, had taken 
place during the first few seconds of the expansion of the universe; 
three years earlier, Bescow and Treffenberg, in Sweden, had pro- 
posed that the elements were originally formed in a sort of gigantic 
"super-star* in gravitational equilibrium. Then, rather unexpectedly, 
the American astronomer Mayall discovered that some stars contain 
appreciable amounts of the element technetium - and this put a 
very different complexion upon matters, because this technetium 
could not be very old. It was already known that technetium is a 
radioactive element, with a half-life of 100,000 years: that is to 
say. in 100,000 years any given amount of technetium will have 
decayed by one-half. There was no escaping the conclusion that 
the technetium in stars was of comparatively recent formation, and 
the principle of uniformity, according to which all the elements 
were formed at the same time, had to be rejected. 

The next step was to find out just how the various elements 
could be produced in a manner which would satisfy the relative 
abundances observed at the present lime. Pioneer work in this field 
was undertaken by Margaret Burbidge, Geoffrey Burbidge, Fred 
Hoyle and W. Fowler, who in 1957 published a lengthy memoir in 
which the whole problem was critically examined. They came to the 
conclusion that element-formation was not due to one single 
event, but was caused by successive events operating alt over the 
Galaxy, and involving what can only be called a "primary sub- 
stance' of unique composition. It must be said, however, that there 



21 



is as yet no evidence in favour of such a fundamental substance. 
The researches of "B2FH*, as the four authors are often called in 
scientific circles, are not concerned with events which may have 
taken place during the first few seconds of the expansion of the 
universe. It is thought more likely that the answers to the problem 
are to be found inside the stars, or upon stellar surfaces. 

Then, too. there have been other attempts to abandon the 
principles of uniformity which have influenced cosmological 
thought. For instance, Tolmann made a careful study of models of 
a non-uniform universe. Unfortunately, the difficulties involved in 
studies of models of this sort are so great that progress has been 
slight, even though the whole concept seems to be decidedly 
promising and will merit further investigation. 

Broadly speaking, it is impossible to summarise the history of 
cosmology without bringing in the very recent discoveries and 
progress is becoming more and more rapid, partly because of an 
improvement in instrumentation and technique, and partly because 
there are more and more astronomers and physicists available. 
There can be no doubt that cosmology has made more progress 
during the past twenty years than it did during the previous two 
hundred. Also, the link between astronomy, astrophysics and 
cosmology becomes closer and closer; we must deal with stellar 
distances, structure and evolution as well as with gravitational 
theories and relativity, and with atomic physics. 

The present book is divided into four main parts. Part two gives a 
description of the Galaxy in which we live, together with the basic 
facts about the structure of the observable universe. The third 
part deals with 'time', both in measurement and in connection 
with the evolution of the universe. The fourth part describes the 
distribution of the galaxies in space, as well as their individual forms 
and characteristics. Lastly, consideration is given to the galaxies 
taken as a whole, in fact, to the universe itself. 



5 The spiral galaxy M51 in Canes 
Venatici- The spiral arms are 
excellently marked and extend for 
a long way from the nucleus. 
Seen from a distance, our own 
Galaxy would be of this kind. 



2 The Galaxy 



23 




On a dull day, with the sky overcast, it is difficult to draw up a 
proper picture of the universe which surrounds us; but on a dark 
night, such as often occurs in southern countries when the celestial 
objects are at their most brilliant, the universe looks fascinating 
indeed. But to allow one's imagination full rein is no obstacle to exact 
knowledge and detailed study, and, after all, Man's first ideas about 
the universe were drawn solely from observation. Theory had to 
come afterwards, and without observation it could not have come 
at all. Therefore, observational mailers must be discussed first. To 
attempt to explain them, we must make full use of our knowledge of 
physics. 

When considering the universe, the problems of matter, space, 
time and movement must be considered in their most fundamental 
aspects. The matter which surrounds us is seen in a variety of forms; 
it is distributed throughout space, it evolves in the course of time, 
and it is not motionless. The essential problem is to separate the 
different forms of matter, and to explain its movements, distribu- 
tion and other characteristics. This cannot be tackled without first 
taking an overall view of what may be observed, and detailed 
analysis must follow this. 

A short description of the universe 

Naked-eye observation, telescopic observation, and (more im- 
portant) photographic studies can tell us a great deal about the 
bodies to be seen in the universe. They can be classified, and it will 
be best to give an outline of this classification at the outset, so that 
the reader will become familiar with the various terms. 

It is logical to begin with the stars, of which about 5,000 are 
visible to the naked eye over both northern and southern hemi- 
spheres of the sky. Telescopes increase this number considerably, 
and immense quantities of stars may be recorded on photographic 
plates. There is a great range in brilliancy, and the stars are 
divided into definite classes or magnitudes of apparent brightness. 
The fainter the star, the greater the magnitude. When two stars 



24 



25 



6 The Milky Way. 



North galactic pole 



Pollux ;__ 

/ JCasior , 



Poiaris 



• \ ''/ * /~< < * ' . ' ■*■'■ v 

'N„ VjfljJS /PERSEUS . S • ■ '--'.' ' Atta ^v ^Jy 

.ORfoNl \T /— — .vygoi • . ; . • • fA/Jf ' 

'VtlSi *,_- NC ■DELPHIn'uS 

*» ^ \ANDRDMEDA 

TRIA%ULUM>-^ , 




South galactic 



North galactic pole 




MJRUS 



^1^^^^/% 






CANIE? 
Procyon# 
^X v>V ■' MINOR 



NORMA 



// MUSGAl. 

trWjgulum; ar T 



RIANGULUM. 
AUSTRALE 



MONOCEROSl 
Sinus 



V . • '"MAJOR- 



South'Celestial Pole' Nubecula Maior 
. ■ % ■ ■ 
Nubecula Minor . (Great Magellanic CJdud I 

(Small Magellanic Cfoodl 



CANOPU6 



Duth galactic pole 



7 Star- clouds in the Milky Way, This is a 
typical rich field showing vast numbers of stars 
together with nebulosity . It is the ki nd of vie w that 
can actually be seen by visual observation with 
an adequate telescope. The apparent crowding 
of the stars is due largely to line of sight effects. 



?*■ 






!>\ 





k?:- 



S&fflSl 




FWw 







:*,* 




m*st 



• *■» *• 



.*• 



:,* - 




• .* r. 




j> 






>'•'! 


a 


•* . 



28 



29 



8 The diagram shows the effects of parallax. Star E' is comparatively remote; 
star E is much closer to the Earth. E ' seems to remain in the same position, but 
E shifts its position over an interval of six months because of the Earth's movement 
round the Sun. Measurement of the angle T, ET 2 gives the star's parallax. In the 
case of Proxima Centauri, the angle is 1 -6 seconds of arc, corresponding to a 
distance of si ightl y over four light-years. 







differ by five magnitudes, the fainter star has only 1/I00 the 
brightness of the more brilliant - that is to say, a star of magnitude 
2 is one hundred times as bright as a star of magnitude 7, and so on, 

Sirius, the brightest star in the sky, is of magnitude —1-4. while 
the faintest star which can be photographed goes down to magnitude 
+23. There is therefore a range of almost 25 magnitudes, with a 
ratio of the order of 10,000,000,000 to 1. The photographic Carte 
<iu del, which goes down to magnitude 13. contains about ten 
million stars, while the Pahmar Sky Atlas, which extends to the 
20th magnitude, includes about a thousand million stars. 

It is obvious at a glance that the stars are unequally distributed 
in the sky. There is a great increase in star-density in the region of 
the Milky Way, the shining band which stretches across the sky and 
which has been known from the earliest times. Actually, the Milky 
Way is made up of a large number of faint stars which cannot be 
seen individually with the naked eye, so giving the impression of a 
glowing band. In other parts of the sky, well away from the Milky 
Way zone, there are far fewer stars. 

A convenient method of studying star-density is to divide the 
sky into small equal areas, counting the number of stars visible in 
each; every unit is a square with its side measuring one degree on 
the celestial sphere. On the whole of the celestial sphere there are 
about 40,000 square degrees, and any preliminary chart constructed 
in this way shows up the unequal distribution. It also confirms the 
results of direct observation of the distribution of the stars in space, 
and the position of our Solar System in the Galaxy. 

The Galaxy itself is made up of about 100,000 million stars 
arranged in the form of an immense disc, with a central condensa- 
tion. When looking along the main plane of the disc, an observer 
sees a great many stars in roughly the same direction, and this 
produces the familiar Milky Way effect; in the perpendicular 
direction, the number of stars visible is much less. 

Hazy, nebulous objects are found here and there among the 
stars. They arc not stellar in aspect, but appear diffuse. The true 
nebulae are clouds of gas mixed with dust; they may look bright, 



30 



9 The magnificent nebula M8 in 
Sagittarius. The gaseous nebula 
is seen in red hydrogen light. 
The luminosity is due to 
fluorescence by the excitation 
of atoms by ultra -violet 
radiation emitted by the star 
at the centre of the nebula. 
Other diffuse nebulosities are 
visible in the photograph. 







32 



because ihey are emitting light, or dark, because ihey absorb light 
and blot out stars lying beyond. The objects formerly known as 
extra-galactic nebulae are in fact galaxies, in every way comparable 
with the Galaxy in which we live; they are enormous systems 
containing vast numbers of stars. The galaxies are of supreme 
importance, because they make up the essential building-blocks of 
the universe. The stars themselves are masses of gas, and they 
collect together into these huge systems which we call galaxies. 

Distance determinations 

When trying to draw up a distance-scale for the universe, the 
Solar System is the obvious starling-point. The Earth moves round 
the Sun in an orbit which has a radius of 93,000,000 mites, or 
150.000,000 kilometres, so that in six months the Earth passes 
through positions which are separated by 300,000,000 kilometres. 
Originally, it was hoped that this displacement would produce an 
apparent shift in the positions of the nearer stars as against the 
more distant objects in the sky; and it is quite true that this shift, 
known as parallax, does occur. However, accurate instruments arc 
needed for the parallax movements to be measured, and nothing of 
the sort could be done four centuries ago. Copernicus realised 
that the apparent lack of parallax shift was no obstacle to his 
theory that the Earth moves round the Sun - provided that the stars 
are extremely remote. Later in the sixteenth century, the great Danish 
astronomer Tycho Brahe put forward counter-arguments. He did 
not believe the stars to be immensely distant, and from this he 
went on to claim that the Earth must lie at rest in the centre of the 
universe. It was not until 1838 that the first successful parallax- 
measure was made, by F.W.Bessel in Germany. 

The nearest known star, excluding the Sun, is Proxima Centauri 
in the southern hemisphere of the sky. Here, the apparent dis- 
placement due to parallax over a period of six months is 1-6 
seconds of arc, so that an observer on Proxima would measure the 
diameter of the Earth's orbit round the Sun as less than 2 seconds 




33 



1 Stars E, E' and E" have the same velocity 

in space and are observed by an observer 

at O. Direction OE"'isthe direction of the velocity 

common to all three stats. The apparent velocity 

against the background becomes less tor 

a star closer to direction OE'". 



of arc. This is very slight; an angle of l second is roughly the angle 
subtended by one centimetre seen from a distance of two kilo- 
metres. Proxima Centauri is about 250,000 times as far away as 
the Sun, and is not visible with the naked eye. 

All measures of star-distances are based upon parallax dis- 
placements, but the actual method can be applied to only about 
10,000 stars; with more distant objects (beyond about 20,000,000 
times the distance of the Sun) the parallax shifts become so slight 
that they are swamped in the unavoidable errors of observation. 

As has been noted, the light-year is a convenient unit for star- 
distance measures. On this reckoning. Proxima Centauri is rather 
over 4 light-years away, while the parallax method can extend out 
to objects at something like 300 light-years. 



11 The Doppler effect, or Red Shift. With an approaching 
body the spectral I ines ate sh ifted toward the blue or 
short-wave end, whereas with a receding body the shift is 
to the red or long-wave end. The diagram is schematic, 
but shows the general principle, which is of fundamental 
importance in all stellar astronomy and cosmology. 





12 The radio telescope at the Tokyo Observatory. 
This is one of the smaller paraboloids, 
fully-steerable. and used mainly 
for solar work. (Photographed in 1966). 



37 



Absolute magnitude 

The apparent magnitude of a star depends partly upon its distance 
and partly upon its real luminosity. The absolute magnitude may 
be defined as the apparent magnitude that a star would have if it 
were observed from a standard distance of 32-6 light-years, that is to 
say at a distance from which the radius of the Earth's orbit would 
subtend an angle of O-l seconds of arc. The absolute magnitude 
of the Sun is 4-62. so that it is neither particularly luminous nor 
particularly feeble. 

Star- streaming 

Another method which has been used successfully in measuring 
the distances of some more remote stars is based on the fact that 
there exist groups of stars which share a common movement in 
space relative to the Sun, and which show the phenomenon known 
as star-streaming. To show how this can be turned to good account, 
it is useful to draw an analogy with a train which is moving along a 
straight track. Objects which lie close to the train appear to shift 
more quickly than objects which are further away; as seen from the 
back of the train, the rails seem to meet at a point in the far dis- 
tance, and while the train is in motion all objects appear to rush 
away along paths which converge toward the vanishing-point. 
On the other hand, an observer at the front of the train will have 
the impression of objects separating from each other and dis- 
appearing to either side of the advancing train. It is easy to see how 
this principle may be applied to the Sun, which may be said to 
stand for the moving train while the other stars represent objects 
such as trees and houses. Each group of stars seems to suffer 
displacement toward a single point, which is called the convergent 
of the stream; the direction in which this point lies is also the 
direction of the apparent movement of the star-group relative to 
the Sun, The distances of the stars in a stream are obtained from 
measuring their apparent shifts and their velocities along the line 



38 



13 Remains of the 72- in Rosse 
reflector at Birr Castle, Eire, This 
telescope was built by the third Earl 
of Rosse in 1 845 and remained the 
largest reflector i n the world for over 
half a century. With it Lord Rosse 
discovered the spiral structure of some 
of the galaxies, including M51, The 
mirror was of speculum metal - it was the 
last really large metal mirror to be 
built - and the mounting was so 
cumbersome that one could examine 
only a limited area of the sky to either 
side of the meridian. The telescope 
was last used in 1908. after which the 
mounting became unsafe and the 
whole structure was dismantled. 
The mirror is now displayed at the 
Science Museum in London ; the tube 
remains at Bin- Castle. (Photographed 
in June 1967). 





40 



41 



of sight. For these latter measurements, use must be made of the 
famous Doppler effect. 

The Doppler effect 

The easiest way to explain the Doppler eflect is to study the be- 
haviour of sound waves. With a moving train which is sounding its 
whistle, the difference in the whistle-note between the approaching 
and the receding part of the line is very obvious; the note is high- 
pitched when the train approaches, and drops when the train nioves 
away from the observer. In other words, the frequency is higher 
with approach, lower with recession, and the relative change in 
frequency is determined by the ratio of the speed of the source to 
the speed of propagation of the sound waves. A sound wave 
moves at about 330 metres per second, so that a train travelling at 
120 kilometres per hour has a velocity 10 per cent of that of the 
speed of sound. The associated change in frequency corresponds 
to an increase of 10 per cent when the train is approaching the 
observer, and to a decrease of 10 per cent when the train is moving 
away - so that there is an overall difference of almost two tones. 
Light, which is an electromagnetic vibration, shows the same sort 
of effect. With an approaching tight source, the frequency is raised, 
while with a receding source the frequency is lowered. Since wave- 
length is inversely proportional to frequency, the receding source 
seems to have the longer wavelength, but of course the effect is 
much less obvious, because light waves move so much more 
rapidly than sound waves. At a speed for the observer of 30 kilo- 
metres per second (about 100,000 kilometres per hour), the wave- 
length is changed only by one ten-thousandth, which is not very 
much. All the same, a luminous source receding at half the velocity 
of light would show a Doppler effect to such a degree that its blue 
radiation would appear red to an observer lying at rest relative 
to the source. One amusing anecdote has been told in this connec- 
tion. An American astronomer was brought before a court, accused 
of driving across a road despite the red traffic-light. He told the 



14 A star-field photographed with the objective prism equipment at Fehrenbach. 
The field was photographed twice on the same plate, each star producing a small 
spectrum - blue on the right (or the upper spectrum, blue on the left tor the lower 
spectrum. This method makes it possible to identify the various spectral lines. 
The H;- and H,j lines of the upper spectrum are approximately opposite the Hy 
and H fi lines of the lower spectrum, but on closer examination it is seen that the 
apparent distance between the H ;■ of the upper spectrum and H o of the lower 
varies from star to star. These differences are due to the fact that the stars have 
different radial velocities so that the Doppler shifts are not the same. 




42 



15 The dome of the 72- in Tautenburg telescope 
This particularly modem type of dome 
houses the 'all-purpose' reflector shown 
in figure 4. (Photographed in 1963). 



judge that he had seen the light as green, owing to the Doppler 
effect - but unfortunately for him, the judge knew just what was 
meant by the Doppler effect, so he waived the fine for jumping the 
traffic-light and fined the motorist for driving too fast! (Of course, 
to have seen the red light as green, the motorist would have had to 
have been driving at about one-third the velocity of light.) 

When the speed of the source approaches the velocity of light, 
there is no straightforward way in which to calculate the change in 
apparent wavelength. To understand this, it is helpful to consider the 
relevant frequency, which is inversely proportional to the wave- 
length, and imagine that the observer is moving at the velocity of 
light. To him, the waves in a pencil of light-rays would appear 
completely stationary, because at each point he would always see 
the same wave - and consequently, the wavelength would be 
infinite! It follows that to an observer approaching the velocity of 
light, all wavelengths from a luminous source will increase in- 
definitely. The necessity of considering such effects, which are dealt 
with in the theory of special relativity, has recently been driven 
home by the discovery of the quasars. This subject will be discussed 
further in Sections 4 and 5 of the present book. 

So far as the stars are concerned, Doppler effects are measured 
by means of spectroscopy. An astronomical spectroscope may be 
said to analyse the light coming from the stars, producing a coloured 
band or spectrum crossed by dark lines; each line is due to some 
particular element or group of elements. In the laboratory, these 
elements can be produced, and their wavelengths measured; the 
identifications are easy in many cases, particularly as the great 
physicist Kirchhoff showed, as long ago as 1859, that each element 
is capable of absorbing radiation of the same wavelength as that 
which it emits. If the spectral lines found with the stars are shifted 
slightly compared with the equivalent lines measured in the 
laboratory, the cause can lie only in a toward-or-away motion ; in 
other words, the Doppler effect. The amount of Doppler effect 
is therefore a reliable way of estimating the real radial movements 
of the stars, and the same principles can be applied to the galaxies. 




The distances of the stars in a stream 



After this slight but necessary digression, let us return to the 
star-streams. For each star in a stream, it is possible to measure the 
proper motion, or apparent individual movement against the back- 
ground of more distant stars, and also the radial motion, which 
is the toward-or-away movement as shown up by the Doppler effect. 
Take, for instance, a star of a stream which is seen at an angle of 
45 degrees to its convergent. The longitudinal (radial) velocity and 
the transverse (proper motion) component are equal. If the velocity 
of the star in space is 42 km/sec, the radial velocity is 30 km/sec 
and the transverse velocity is also 30 km/sec, the apparent shift 
in position over a period of ten years will be 2-06 seconds of arc, 
so that its annual proper motion will be 0-206 seconds of arc. The 
distance of each star in the stream can then be worked out very 
accurately. This method has been applied successfully to an 
important group of stars in the constellation Taurus, known as the 



44 



45 



Hyades cluster. The group lies at about 120 light-years from the 
Sun, and has a velocity, relative to the Sun, of 44 km/sec. By now, 
the distances of 159 individual stars in the Hyades have been 
determined with great precision, and this means that the absolute 
magnitudes can also be found, Therefore, the Hyades may be used 
as standards of reference for other groups, lying further away and 
consequently more difficult to measure directly. 

Variable stars 

As has been noted, there are some stars which show short-term 
variations in brilliancy, and of these the most important are the 
Cepheids, whose periods are short (from a few days up to several 
weeks) and whose behaviour is quite regular. In 1912, Miss 
Henrietta Leavitt. at Harvard, made a discovery which proved to 
be fundamental in the determination of stellar distances. She was 
studying Cepheids in the Small Magellanic Cloud, which is a 
southern-hemisphere object, and which is one of two minor 
galaxies associated with our own. Because the Cloud is relatively 
remote, all the various objects in it may be effectively regarded as 
being at the same distance from us, and Miss Leavitt found that the 
Cepheids with the longer periods were always the brightest - which 
meant that they must also be the more luminous. This was. of 
course, the first inkling of the Cepheid period-luminosity law. It 
is certainly valid, and it means that the distance of a Cepheid can 
always be worked out as soon as its period of variation is known. 
The only real problem is to find an absolute-magnitude scale. 
Unfortunately, all Cepheids are relatively distant, so that their 
parallax shifts are too small to be measured. 

A related class, made up of variable stars with very short periods. 
has been found to be most useful in this connection. These stars 
are known as RR Lyra variables, after the prototype example RR 
Lyrae, which fluctuates between magnitudes 7-1 and 7-8 in a period 
of 0-57 day. All RR Lyrse variables have approximately the same 
luminosity, so that all that needs be done is to measure their 



1 6 The convergence of stars in Taurus. The positions of stars in the Hyades 
cluster are shown. Each star has a small arrow whose length is proportional to 
the star's annual proper motion. All the arrows converge toward the same point. 
Just as the lines of a railway track seem to meet near the horizon {assuming that 
I he track is straight), so the convergence of the arrows shows that the stars have 
parallel paths in space. The direction toward which the arrows are converging is 
of course the d irection of the stars. 






•o* 






_• i i i i i i i ■ ' 



121 
f17° 

5 



6h 



5h right ascension (ex) 4h 



apparent magnitudes; since the luminosities are equal, the brighter 
stars will be the closer to us. As they are in motion relative to the 
Sun, a method much the same as that used in star-streaming can 
be applied to the RR Lyrse stars considered as a class. The direction 
of movement of the stars relative to the Sun is known. Stars lying 
in a direction perpendicular to the direction of their motion 
relative to the Sun will show proper motions against the celestial 
sphere, which can be measured; stars lying along the line of the 
Sun's relative motion, in either direction, will have measurable 






46 17 The 98- in Isaac Newton reflector, taken in 1 965, when 

the telescope was under construction at Newcestle-on-Tyne. 
The mirror is not in the tube, but the general pattern of the telescope 
stands out well. The telescope is now in operation at the 
Royal Observatory at Hurstmonceaux. in Sussex It is by far the 
largest telescope in Britain, and the fifth largest in the world. 

radial velocities. By comparing the mean proper motions and the 
mean radial velocities, and knowing that differences in apparent 
magnitudes must be due to differences in the real luminosities of 
the stars concerned, the absolute magnitudes of the RR Lyrae 
variables can be worked out very accurately. At the standard 
distance of 32-6 light-years, an RR Lyra; star would appear 
bright, with an apparent magnitude of 0, so thai it is about one 
hundred times as luminous as the Sun. 

Distance determinations for the Cepheids, which have longer 
periods and which are more powerful, can be carried out by much 
the same method, and here too the absolute magnitudes can be 
found; for instance, a Cepheid with a period of 100 days has an 
absolute magnitude of about —5. There is no real difficulty about 
studying Cepheids down to an apparent magnitude of +20 or so. 
It is known that a difference of 25 magnitudes corresponds to a 
distance ratio of 1 :100,000. Therefore, if a star of absolute mag- 
nitude —5 appears to be of apparent magnitude +20. its distance 
must be 3,260.000 light-years. 

This technique must depend upon a theory about the nature of 
the stars, because the statement that Cepheids of the same period 
have the same intrinsic brightness is tantamount to saying that they 
must have had a similar origin and have gone through the same 
phases in evolution. It is now known that variability is a characteris- 
tic which occurs for only a relatively short period during a star's 
career, a very long time after the star was formed: also, not all 
stars become variable at any particular stage. It is true to say that 
a star in the process of formation 'does not know' whether it will 
ever become a variable, or whether it will not ; also, stars at an early 
stage in their evolution give us no clue as to whether they are 
likely to go through a variable stage. Yet it seems certain that 
Cepheids of equal period must be essentially similar to each other, 
and must have developed along the same lines. 




48 



18 The Large Magellanic Cloud. It is 
a galaxy visible from the southern 
hemisphere and appears to be a true 
companion of our own Galaxy. 



The distribution of stars in the Galaxy 

As has been noted, the stars in the Galaxy are arranged in the form 
of a disc; the Sun, of course, lies within this disc. In a direction 
along that of the plane of the disc, the number of stars per square 
degree is very great; at a direction right-angles to the main plane, 
the apparent number of stars per unit area is much less. To com- 
plete this description, something should be said about the distances 
of the stars; the short-period variables have been of immense 
importance in this connection, and it has been possible to show, 
with pleasing accuracy, that the Sun lies about 30,000 light-years 
from the centre of the Galaxy. 

By means of absolute-magnitude determinations (notably by 
spectroscopic methods, of which more will be said later), and by 
straightforward counts, it has been possible to determine the 
distribution of the stars in space in the neighbourhood of the Sun. 
For all types of stars, the density-rate falls off with increasing 
distance from the plane or the Galaxy, as is only to be expected, 
but each variety of star has its own characteristic distribution with 
regard to the mean distance of the group from the galactic plane. 
Considering that most of the stars lie within a region only about 
300 to 400 tight-years in thickness, there is a wide range in the 
depths of zones occupied by the various star-types. For example. 
the blue dwarfs lie within about 1 50 light-years to either side or the 
plane. The Sun (a yellow dwarf) is situated almost exactly on the 
main plane. 

The fact that the stars are not all distributed in the same way 
throughout the Galaxy may be explained quite simply in terms of 
elementary laws of celestial mechanics. What must be done first is 
to consider the forces which operate in the Galaxy as a whole. 



Gravitation 

In the latter part of the seventeenth century, Sir Isaac Newton 
showed that the attraction between two bodies is proportional to 



50 19 The North American Nebula. NGC 7000 Cygrti, 

photographed with the 48 -in Schmidt at Palomar. 
This is contained in our Galaxy and is not an 
external system. Its nickname is derived from its 
shape, but long-exposure photographs are 
needed for it to be seen to advantage. 



the product of their masses and inversely proportional to the 
square of the distance between them. Yet this force is surprisingly 
small. For instance, the Moon will attract an object on the Earth's 
surface with a force only 1/300.000 of that due to the Earth itself. 

Weak though it may be. this force is the cause of the stability of 
celestial bodies; and because of it, the velocity needed for an object 
to escape from the Earth is 11,200 metres per second (roughly 
7 miles per second). To escape from the Solar System, starting from 
a distance from the Sun equal to the radius of the Earth's orbit, an 
object would have to be given a starting velocity of over 43 kilo- 
metres per second. It is because of gravitation that the stars in our 
Galaxy make up a definite system. 

The shape of the Galaxy is the result of equilibrium between 
gravitation and centrifugal force. Each star moves in the gravita- 
tional field of all the others; thus the Sun turns around the centre of 
the Galaxy with a velocity of about 250 kilometres per second, 
completing one revolution in roughly 250,000.000 years. To escape 
from the Galaxy, a star staying near the galactic plane would have 
to be given an initial velocity of at least 380 kilometres per second. 
Such relatively great velocities account for the flattened shape of 
the Galaxy. If a star-system does not rotate, it will not acquire a 
flattened shape. The spherical or nearly spherical systems which are 
known lo exist near our Galaxy must have this shape either because 
they rotate very slowly, or because they do not rotate at all. 

Consider next a star which does not lie near the galactic plane. 
It is obviously attracted by a force which is perpendicular to the 
plane, and directed toward the Galaxy. If its velocity in the 
direction perpendicular to the plane is small, it will not be able to 
move far from the plane; but if it has a high velocity in the direction 
perpendicular to the plane, it will be able to follow an orbit which 
will extend well outside the Galaxy. The differences in distribution 
of the stars in space are therefore of dynamical origin, but. as will be 
shown later these dynamical differences are associated with 
physical differences among the stars concerned. 



B .."■■ - * Kr 
■/■- • 



;->.-S. *' 






•V ' I" 



•■•.'. ■'.• ' 






-v ■ ■ ' 






52 



Dwarfs and giants 

The colour at the fire-hole of a furnace depends upon the interior 
temperature; il may be blood-red, cherry-red or white, in order of 
increasing temperature. In other words, the higher the temperature, 
the greater is the proportion of blue radiation compared with red, 
so that the proportion of short-wave to long-wave radiation in- 
creases with the temperature. Generally speaking, this is also true 
for the stars, whose colours are dependent upon their surface 
temperatures. A star's colour is measured by what is called its 
colour index, related to the ratio of blue to red radiation which is 
emitted. Red stars have a positive colour index; with blue stars, the 
colour index is negative. 

Two essential facts must be known before a star can be put into 
its proper classification. One. already described, is the absolute 
magnitude; the other is the colour index. When the stars are plotted 
on a diagram according to their absolute magnitudes and colour 
index, it is at once clear that the stars are not scattered in a hap- 
hazard manner. Most of them tie near a line which crosses the 
diagram diagonally, and is called the Main Sequence. 

A star cannot be plotted on the diagram unless its distance is 
known, A small number of nearby stars for which the parallax 
method is applicable can be very useful here, and the diagram for 
them is shown; but the stars of the Hyades, described earlier, are 
better known as a class, and. as noted, arc used as reference 
standards in the calibration of the relationship between absolute 
magnitude and spectral type. 

It has already been stated that the spectrum of a typical star is 
made up of a rainbow background crossed by dark absorption 
lines, each line being due to a particular element or group of 
elements. Another method for estimating stellar luminosities is 
that of studying the relative intensities of certain spectral lines, 
which, like the star-colours, depend upon surface temperature. In 
fact, there is a close relationship between the temperatures and the 
details of the spectra. 



20 The light-curve of Delia Cepbei The magnitude range is from 3 6 to 5 1. 
with a period of 5 37 days. In other words, the star is 2-3 times brighter at 
maximum than ai minimum. Cepheids are pulsating stars, which alternately 
expand and contract like a balloon. During their cycle of evolution, 
some stars pass through a 'variable' stage, which lasts for some thousands 
of millions of years. Cepheids are variable stars of this kind. 



41 


i i i i i i i i i i i i i i 


•a 

3 

'E 

O) 

fa 

£ 


• 


■ 
*• 

• 


•%.. 


T* 


/ V. 
• •• 

; x. 

• *■■• . 
t i 




i i i 


i i i i i i g i i i 


i 



5 37 days 



The initial discovery was that of a link between absolute magni- 
tude and spectral type; this resulted in the well-known Herlz- 
sprung- Russell or H/R diagram, named in honour of E.J. Hertz- 
sprung of Denmark and H.N.Russell of the United States. It 
closely resembles the diagram shown in figure 28. The advantage of 
the colour index/absolute magnitude diagram is that it is more 
precise; classification of a star's spectrum is always less exact. 

The spectral types of stars are given by different letters. Stars of 
type B are blue; type A stars are white, F and G yellow, and K and 
M red. It has already been noted that B-type dwarfs lie at a mean 
distance of about 150 light-years from the galactic plane, but it 
should be added that all normal B-stars are much hotter and more 
luminous than our Sun, so that the term "dwarf is somewhat 
misleading when applied to them. A dwarf star has a radius 
comparable with that of the Sun, and the radius depends upon the 
absolute magnitude to only a limited degree; thus a star with a 
luminosity 10,000 times that of the Sun may have a radius only 6 
times as great, while a star with a luminosity of 1/10,000 that of the 
Sun will have a radius of one-third that of the Sun. Along the 



21 The Pleiades photographed in colour from Palomar, Every 
astronomical enthusiast knows the 'Seven Sisters' but in fact 
the cluster contains many members, together with a nebula 
which shows up well only with long-exposure photography. 
The nebula is of the reflection type, that is. it shines only 
because it is lit up by the stars mixed up with it. 



55 





22 A diagram of the shape of the Galaxy. The stars, with the 
interstellar gas, form a vast flattened disk with a diameter 
of about 1 00,000 light-years The Sun lies approximately 
in the main plane, at a distance of 30,000 light-years from 
the centre. Asterisks indicate the positions of globular clusters - 
huge collections of stars which move round the Galaxy. 




100,000 



Main Sequence, we therefore find stars with a brilliancy range of 
100,000,000 to 1, but a range in radius of only about 20 to 1. With 
two stars of the same colour index but different luminosity, the 
more brilliant star will have the larger radius. 

Stars with radii much larger than those of the Main Sequence are 
known as giants. They are of immense size, and may have radii 10, 
100 or even 1,000 times greater than the Sun's. The region in the 
H/R diagram containing stars of large positive colour index and 
high luminosity is the region of the red giant and supergiant stars. 
Red giants are found in large numbers in the globular clusters 
which lie near the boundary of the Galaxy, and in general there is 
a close relationship between the intrinsic properties of the stars and 
their motions, because the distribution of the stars in space is 



57 



' 



related to both. There is an important distinction between stars 
such as the red giants, well away from the galactic plane, and 
ordinary stars of the Main Sequence, which are in general scattered 
around the neighbourhood of the plane. 

Spectroscopically, giants are easily distinguished from dwarfs 
because the absorption lines are much thinner. When the spectrum 
of a star can be examined in sufficient detail, there is little difficulty 
in working out its type, its colour, its place in the H/R diagram and 
its position in the colour index/absolute magnitude diagram. In 
many cases this is the only known means of determining the 
absolute magnitude of a star, and hence its distance. Distances 
worked out by this method of spectroscopic parallax are naturally 
rather uncertain, because one can never be sure that the derived 
luminosities are wholly reliable, but in general the method is a 
satisfactory replacement for ordinary or trigonometrical parallax 
measurement. However, care must be taken to avoid reasoning in 
a circle. The Hertzsprung-Russell diagram was compiled by using 
stars of known distance, but the diagram itself is used to measure 
the distances of stars for which other methods fail. 

This method of spectroscopic parallax has been of fundamental 
importance in fixing the positions of the stars in space. For 
thousands of remote stars, no other means can be used. It is in this 
way, then, that it has been possible to classify the stars into different 
types, according to their distances from the main plane of the 
Galaxy. Essentially, the stars close to the galactic plane are of what 
is termed Population 1. while stars well away from the plane belong 
to Population II. Generally speaking. Main Sequence stars are of 
Population I, red giants of Population II; it is also true to say that 
young stars belong to Population I, old stars to Population II. 

Gas and dust 

Great masses of dust and gas can be seen in the Galaxy. The gas is 
visible because it is luminous, while the dust absorbs the light of 
more remote stars and so betrays its presence. For instance, it is 



58 



23 The solar dome at the Crimean Astrophysical 
Observatory. USSR. The main equipment, 
designed by Or Severny. is contained in 
this dome. (Photographed in 1 960). 



well known that in ihc southern hemisphere of the sky, the Milky 
Way apparently splits into two branches. However, this division 
is not real; it is due to the presence of a large, dense dust-cloud 
relatively close to the Solar System (close, that is to say, on the 
cosmica) scale!) which absorbs the light from the stars behind it. 
Dust is very efficient at absorbing light, and in the plane of the 
Galaxy it causes the apparent magnitude of a star to increase by 2 
for every 3,000 light-years; thus a star 6,000 light-years away from 
us will appear two magnitudes fainter than it would otherwise do, 
while a star in the centre of the Galaxy will have its magnitude 
increased by 20 because of the dust absorption. A further 15 
magnitudes must be added on account of the star's distance, and 
so the absolute magnitude must be increased by 35 to obtain the 
apparent magnitude that the star would have if it could be observed 
at the centre of the Galaxy. Since stars of magnitude greater than 
+ 23 are too faint to be photographed, a star lying at the galactic 
centre would have to be of absolute magnitude — 12 or more to be 
observable. No star as luminous as this can exist, aod it is evident 
that the dust hides the centre of the Galaxy completely so far as we 
are concerned. 

The bright nebula account for only a small fraction of the total 
mass of gas in the Galaxy. Generally speaking, the nebula; shine 
because they are affected by ultra-violet radiation sent out by hot 
stars close to them. This ultra-violet radiation acts on the atoms 
making up the gas. and excites the atoms to a level at which they 
emit light. Analysis of the light makes it possible to find out the 
chemical composition of the nebulae. 

Visual observations of the absorbing gases and the luminous 
nebula: show that the gas and dust clouds are spread out close to 
the galactic plane. As will be shown later in this book, there is 
nothing fortuitous about the similarity between the distribution of 
the gas and dust, and the distribution of most of the stars belonging 
to the Main Sequence, 

Recently-developed techniques have led to important discoveries 
about the Galaxy. Consider, first, the classic diagram which shows 




24 Part of the Milky Way in 
the southern hemisphere. Note 
the dark obscuring mass of gas 
close to the I wo brightest stars. 



61 



the so-called electromagnetic spectrum, or total range of wave- 
lengths, ranging from very short wavelength X-rays up lo long- 
wavelength radio waves. Extremely short wavelengths are measured 
in Angstroms or microns; one Angstrom is equal to one ten- 
millionth of a millimetre, while one micron is equal to one- 
thousandth of a millimetre. X-rays may have wavelengths of no 
more than 1 Angstrom, which is small by any standard. The human 
eye is sensitive only to the narrow band in the electromagnetic 
spectrum between 04 and 0-8 microns. The photographic plate 
extends this range by about 2 microns toward the longer-wave 
end. and in theory it should provide a greater extension toward 
the ultra-violet, but unfortunately this extension is theoretical only, 
because all the ultra-violet and X-rays coming from the sky arc 
blocked out by the Earth's atmosphere. The situation is a little 
better on the infra-red side of the "optical window 1 , where wave- 
lengths in the millimetre and decametre range can pass through 
the atmosphere more or less unobstructed; but still longer radia- 
tions, with wavelengths in the kilometre range, are completely 
blocked. However, the 13 or 14 octaves accessible in the "radio 
window" have led to a great deal of extra information about the 
Galaxy. Observations from ground level have been very successful, 
thanks to the new equipment which has been developed during the 
past twenty years. On the other hand, the short-wavelength radia- 
tions cannot be studied by means of instruments set up on the 
Earth's surface, and there is no choice but to send up the equipment 
in rockets, artificial satellites, or (for convenience) high-altitude 
balloons. 



Radio radiation (lines) 

Radio emission provides a continuous background emission 
together with a line spectrum. The continuous emission is of an 
intensity which changes slowly with wavelength, and there are 
very few definite spectral lines. At the present moment one strong 
emission line has been detected; it is caused by atoms of hydrogen, 



62 



25 The planetary nebula NGC 7293 in Aquarius, photographed 
with the 48-in Schmidt telescope at Paiomar This is a relatively 
bright planetary, comparable with the Ring Nebula in Lyra ; 
it is also the same kind, though less symmetrical. For some 
reason it was not included in the original catalogue of nebulous 
objects drawn up in the eighteenth century by Messier. 



63 



and has a wavelength of 21 cenii metres. Several weak lines of 
hydrogen have also been detected. There is also an absorption line 
at 18 centimetres, due to molecules of OH (oxygen combined with 
hydrogen). These lines were discovered by observation after their 
existence had been predicted by physicists. The 21 -centimetre 
hydrogen tine has proved to be of particular importance, both in 
atomic physics and in studies of the structure of the Galaxy. 

The discrete emission or absorption of radiation corresponds to 
a change in the energy-state of an atom. The atom of hydrogen, for 
example, consists of one proton and one electron; the transition 
which produces the 21 -centimetre line is caused by a change in 
the energy level affecting both particles. Both the proton and the 
electron have axial rotation, and this gives rise to measurable 
magnetic effects. According to whether the magnetic moments of 
the electron and the proton are in the same or in the opposite 
direction, the energy of the hydrogen atom will be slightly different, 
and this admittedly very slight difference between the two states of 
the hydrogen atom accounts for the 21 -centimetre line. The 
mechanism involved is basically very simple. Atoms of hydrogen in 
interstellar space collide, with increase of energy; the return to a 
lower energy-level is accompanied by the emission of radiation at a 
wavelength of 21 centimetres. The study of this line leads to a very 
accurate knowledge of the distribution of hydrogen atoms in the 
Galaxy, and maps of the hydrogen clouds can be drawn up. The 
density of the hydrogen atoms is, at maximum, 2 or 3 per cubic 
centimetre; the denser clouds stretch through the Galaxy rather 
in the manner of huge arms. Visual and radio researches agree in 
showing that the hydrogen clouds are spread out in the neighbour- 
hood of the galactic plane. 

The structure of the Galaxy has been satisfactorily studied for 
the region lying at more than 10,000 light-years from the galactic 
centre. However, the 2 1 -centimetre investigations have shown that 
totally different conditions occur near the actual centre. Inside a 
sphere with radius about 600 light-years there is a mass of hydrogen 
in a stale of violent agitation, with velocities reaching 200 




26 Th e e I ect ro ma g netic spec tr u m . The ba nd 
below the diagram shows (he extent of atmospheric 
absorption for the various wavelengths. 
Above 25 km the atmosphere is transparent for 
wavelengths shorter than 20 A. 



ii. ii 
angstroms 

* ; 



angstroms 



visible 



-r 



i ' i ■ i ■ i 



i ■ i 



-r 



-r 



~r 



-r 



-r 



-r 



T 



250 t 4 16 62 125 2501000-4 -8 3-1 12-5 50 200 800 3-1 1-25 5 20 80 3-1 12-5 50 200 







N 




H 2 H 2 H 3 

CO, 



ionosphere 



kilometers per second; there is also a general expansion at a rate ot' 
about 50 kilometres per second. The quantity of hydrogen in this 
central region has about 30 or 40 million times the mass of the 
Sun, and its expansion corresponds to a flux of material of about 
one solar mass per year. 

Radio radiation (continuous emission) 

Two kinds of continuous emission have been identified, and have 
been named thermal and non-thermal. Thermal emission results 
from encounters between electrons and ions (an ion being part of 
an atom that has been broken up). Electrons are of relatively low 
mass, and are negatively charged. When they move close to a more 
massive ion which is positively charged, the electrons will undergo a 
"braking' effect, and will emit radiation. So long as the electrons 
owe their velocities to thermal agitation, their emissions will be of 
a characteristic kind, and the resulting radiation will depend upon 
the properties of the electrons which are being affected by the 
thermal agitation. On the other hand, the character of the emission 
changes completely as soon as the motions of the electrons become 
in any way regular, and in this connection the effects of magnetic 
fields are of vital importance sd far as radio astronomy is con- 
cerned. When moving in a magnetic field, an electron turns around 






27 The two states of the hydrogen atom concerned with the emission of the 
21 -cm line. To the left, the magnetic moment ol the proton and the 
electron are parallel and in the same sense ; to the right, the sense is opposite. 
During transition from one state to the other, a certain amount of energy is 
emitted in the Form of electromagnetic radiation and this produces the 21 -cm line 



; > ( t 

p* / \ p+ 



p+ 
^ - 



\ 

2 



the lines of force, and the centrifugal force is compensated by the 
so-called Laplace force (that is to say, the action of a magnetic 
field upon a moving charge). The electron suffers acceleration, and 
emits radiation. In this case, obviously, the movement or the 
electron is being controlled by the magnetic field, so that its radiation 
is easily distinguishable from that due to braking in the vicinity of 
a positively-charged particle. The radio emission caused by spiral 
movement in a magnetic field is very intense, with high-energy 
electrons, and is comparable with the energy of cosmic-ray particles. 

This new type of radiation was detected by the use of machines in 
which high-energy electrons are forced to circulate in a magnetic 
field. Its official name, synchrotron radiation, is taken from the name 
of the machine in which it was originally found. 

Synchrotron radiation is therefore very different from thermal 
radiation. The latter is characterised by the fact that its intensity falls 
off rapidly both for very long and for very short wavelengths. The 
non-thermal radiation of high-energy electrons is quite different; 
the intensity decreases in a very regular manner from radio wave- 
lengths through to the visual band and beyond, perhaps as far as 
the X-ray region. 

Both types of radiation have been detected in the Galaxy. 
Thermal emission is associated with the presence of ionised hydro- 
gen, and is observed chiefly in the decametre band. It shows that 



28 A colour -magnitude diagram for the 
Pleiades cluster. The Main Sequence is 
clearly shown. The diagram is printed 
in colour to emphasise the dominance 
of blue to the left of the diagram 
and the dominance of red to the right. 



67 




V 






-L 



"» 



J_ 




J_ 



-4 -2 



0-4 08 

B-V 



12 1-6 



the distribution of the gas responsible for the emissions is much 
the same as the general distribution of gas throughout the Galaxy. 
However, the non-thermal emission is associated with individual 
objects, the discrete radio sources, formerly (and most mislead ingly) 
known as radio stars. Some of the discrete sources lie outside our 
Galaxy, and will be discussed in part 5. Others are contained inside 
the Galaxy; of these, one of the most important is the Crab Nebula, 
a mass of gas in the constellation of Taurus (the Bull). It lies at a 
distance of about 4,000 light-years, and is almost 5 light-years in 
diameter: it has an emission spectrum in the optical range, in which 
lines of hydrogen, oxygen and nitrogen are prominent, and it also 
shows a non-thermal radio spectrum. The Crab Nebula is a re- 
markable object, and is known to be the remnant of a supernova. 
In 1054, Chinese astronomers observed a new star which became so 
bright that it could be seen in broad daylight, and remained visible 
for several months before fading away. The present-day Crab 
Nebula is all that remains of this tremendous explosion ; not sur- 
prisingly, the spectrum is of a very unusual type. 

As well as these discrete sources, weak non-thermal radio 
radiation occurs almost everywhere in the Galaxy, and gives 
evidence of the existence of high-energy electrons and magnetic 
fields in the space between the stars. The central region of the 
Galaxy contains a source or thermal emission with a diameter of 
about 30 light-years, together with a non-thermal source of about 
Ihesamesi/c. 

X-rays 

X-ray detectors can be flown in high-altitude rockets, so providing 
material for a map of the X-ray emission from the sky. Various 
X-ray sources have been detected in this way. of which one of the 
strongest is the remarkable Crab Nebula. Therefore, the spectrum 
of the Crab extends from the radio range right through the optical 
band through to the very short X-radiations. An even stronger 
X-ray source has been located in the constellation of Scorpio. 



Table 1 Radius of gyration of protons moving in a 
magnetic field of strength one- millionth of a gauss 



Energy 

(electron volts) 
1 

1,000 

1 ,000.000 

10' 

10" 

10" 

10" 

10" 



Radius of gyration 

1 ,400 kilometres 
45,000 kilometres 
1,400.000 kilometres 
0-38 astronomical units* 
220 astronomical units 
3-5 light-years 
3,500 light-years 
3,500,000 light-years 



* One astronomical unit is I ho distance between the Earth and the Sun. 
150.000,000 kitomeires ■ 93,000.000 miles m SOOhght-seconds. 
10 b gauss is the ofdat of magnitude of the galactic magnetic field. 



Cosmic rays 

Studies of our Galaxy and external systems cannot be separated 
from researches into cosmic rays, which are not true rays at all, but 
are high-velocity atomic particles (mainly protons) with energies 
greater than 1,000 million electron volts. The total flux of the 
particles which reach the Earth with energies of over 5.000 million 
electron volts is about 0-2 particles per square centimetre per 
second. The distribution of the energy of these particles shows a 
very regular decrease; the flux falls off as the I -7 power of the energy. 
and this decrease continues up to very high energy levels. Particles 
with energies as high as 10 ao electron volts have been detected. As 
will be shown below, weak magnetic fields seem to be present 
everywhere in the Galaxy, and we must next discuss the motions of 
charged particles in a magnetic field. 



29 The radio interferometer at the Mullard Radio Astronomy Observatory in 
Cambridge. Not all the equipment can be shown in one photograph, for it covets 
a considerable area. With an interferometer of this sort, the greater the area the 
greater the resolving power. The interferometer is not, of coutse. steerable in the 
same way as the Jodrell Bank paraboloid, but in its own way it is equally 
valuable. (Photographed in 1964). 




Movements of particles in a magnetic field 

Electrically charged particles move around the lines of magnetic 
force, so that the centrifugal force is balanced by the Laplace 
force. The radius of movement depends upon the charge, the mass 
and the velocity of the particle concerned, together with the 
strength of the magnetic field. For a proton moving in a magnetic 
field of I0 -6 gauss, the radius of gyration is summarised in table 1. 
The gauss is the unit of intensity of a magnetic field; the magnetic 
induction at a given point is I gauss when the maximum electro- 
motive force that can be induced in a conductor 1 cm long moving 
through the point with a velocity of 1 centimetre per second is one 
unit of electromotive force. 

Clearly, particles with energies of the order of 10 fl electron volts 
cannot escape from the Galaxy, because their radii of gyration are 



70 



30 The Trifid Nebula, M20 in Sagittarius, photographed with the 200- in Hale 
reflector at Palomar. This is a magnificent example of its type, and even a small 
telescope will show it, but as in most other cases, long-exposure photography is 
needed to show the fine structure. Moreover, the Nebula lies in the southern part 
of the sky, and is always inconveniently low when viewed from Britain and most 
of the United States. 



too small, bui particles with energies of the order or I0 !8 electron 
volts cannot stay permanently in our Galaxy. Since we must also 
take non-uniform magnetic fields into consideration, it is found 
that particles of energy well below this value can also escape under 
suitable conditions. 

Charged particles move in spiral paths when in a uniform and 
constant magnetic field. If the field is constant but subject to slow 
variation from one region of space to another, the movement of the 
particle becomes more complicated. When it moves toward a 
region of higher intensity of the magnetic field, it will travel 
parallel to the lines of force, slowing down as it docs so. This 
slackening in velocity will continue until the moment when the 
direction of travel is reversed. Regions where the magnetic field is 
strong enough to cause this effect act as reflecting media, and are 
often called magnetic mirrors. 

in a magnetic field which changes slowly with time - slowly, that 
is to say. compared with the time needed by the particle to complete 
its journey round the field a particle will be affected by a weak 
inductive magnetic field which will modify its path, making it 
travel across the lines of force. 

The phenomenon of reflection at regions where the magnetic 
field is sufficiently intense, together with the effects of motion 
across the lines of force, greatly complicates the movements of all 
charged particles which encounter intense or variable magnetic 
fields. This complicated random motion of a large number of 
particles is what is termed the phenomenon of diffusion. 

Under these conditions, the movements of panicles are com- 
pletely random in direction. If a group of particles starts oft? from 




any given point, they will scatter in all possible directions. For the 
sake of clarity, suppose that the particles are able to move only by 
units of length / in any direction. After N displacements, the 
arrival points of the particles will be scattered over the inner 
surface of a sphere of radius /,/N. if the velocity is v, then each 
movement will need a time (//i')=to, and N movements will be 
completed in a time Nt . The distance R will be covered after 
(R//) 2 =N movements, taking up a time (R 2 //v), With cosmic ray 
particles, the distances / are of the order of 30 light-years, and 



72 



the velocities approach the velocity of light. Cosmic rays would 
take something like a thousand million years to diffuse through a 
sphere of radius 50,000 light-years. This means that the cosmic 
ray particles cannot be permanent members of our Galaxy, and 
there must be some process whereby they are constantly renewed. 
This problem will be discussed later. 

The magnetic field of the Galaxy 

The strength of the general magnetic field of the Galaxy may be 
estimated in several ways. The oldest and best of these concerns 
the polarisation of starlight, which is important enough to be 
discussed here in some detail. 

The polarisation of light 

Light has properties both of wave-motions and of corpuscles. The 
classic work of Clerk Maxwell in the nineteenth century showed 
that the wave properties of light can be well represented by the propa- 
gation of an electric field and a magnetic field, perpendicular to each 
other and perpendicular to the direction of the light-ray. At a fixed 
point, the electric field and the magnetic field oscillate at the fre- 
quency of the radiation; it is, of course, the electric field which acts on 
suitable receivers, such as the human eye or the sensitive plate. The 
direction in which the electric field vibrates is one of the characteris- 
tics of the radiation. If the electric vibrations are orientated that 
is. constantly aligned along one particular direction instead of 
being distributed at random - the light is polarised. Ordinary light 
is the result of the superposition of large numbers of waves 
vibrating in random directions. When one direction of the electric 
field is of higher intensity than the others, the light is partially 
polarised; this too is observed in nature. 

It has already been noted that tight can be emitted because of the 
movements of electrons. When these movements are due simply to 
thermal agitation, the light is non-polarised, and is called thermal 



31 A diagrammatic representation of 
the motion of a charged particle 
in a non- uniform magnetic field. 



73 







74 



32 The Horse's- Head Nebula, NGC 2024 in Orion, near the star ZetaOrionis, 
photographed with the 48 ■ in Schmidt telescope at Palo mar. The dark nebula has 
a slight resemblance to a knight in chess- hence the nickname. There is no 
difference between a luminous and a dark nebula except that in a dark nebula 
there are no stars suitably placed either to light it up or to make it luminous. 



radiation. Bui radiation due to the spiralling of electrons in a 
magnetic field comes from an anisotropic source and is strongly 
polarised, Polarisation can also be produced when radiation 
crosses a medium with anisotropic characteristics. 

Interstellar polarisation 

In 1948 it was (bund thai starlight is slightly polarised. This 
phenomenon is rather surprising, because there seems no reason 
why a star, which is a symmetrical sphere, should emit polarised 
radiation. The only possible solution is to assume that the polarisa- 
tion is due to (he journey made by the light-rays across interstellar 
space. The only force capable of producing effects of this sort 
appears lo be a magnetic field; yet how can a magnetic field act in 
such a way ? 

The absorption of light in space is due lo the presence there of 
fine dust, and the anisotropic properties must presumably be the 
result of the action of Ihe magnetic field upon this dust. Nothing 
definite is known about the chemical composition of the dust, but 
it is certain that atoms of iron, oxygen and silicon, together with 
various types of molecules, exist between the stars, so that the dust 
is presumably a conglomerate of indefinite com position, which 
comes together because of the random encounters between different 
kinds of atoms and molecules. Under such conditions it would be 
thought that the dust particles should be spherical, in which case 
there would be no orientation in a magnetic field; it is not easy to 
see how such conglomerates could have developed into needle-like 
or plate-like forms. On the other hand, various chemically pure 
bodies have different properties. Laboratory experiments have 
shown that (here are at least two examples of small crystals with 
very marked anistropy, which develop naturally; in a rarefied 
atmosphere, atoms of iron can collect to form needles, white 
carbon condenses naturally into plates of graphite. Therefore, it 
is possible that part of the interstellar dust is made up of micro- 
crystals of graphite, which would be orientated by the magnetic 




76 



Table 2 

Rotation of the plane of polarisation (in degrees). 
Magnetic field of 10 'gauss. 
Electron density of 0-1 electron per cubic centimetre. 
Path-length of 3-26 light-years {= 1 parsec). 
Wavelength (in metres). 



Rotation 



01 

0*465 



10 

4650* 



field. Under these conditions, polarisation would occur. 

The particles must have dimensions of the order of one micron 
(one-thousandth of a millimetre). After the journey across inter- 
stellar space, the electric field of the radiation parallel lo the 
magnetic field has become very weak, so that the interstellar dust 
is responsible for partial polarisation. Measurements of the 
polarisation produced indicate that the strength of the general 
magnetic field in space is about one-millionth of a gauss. 



Synchrotron radiation 

ll has already been noted that there are important spectral dif- 
ferences between radio waves of thermal origin and synchrotron 
radiation. This means that the two types of radiation can be 
distinguished in the general emission coming from the Galaxy. 
With wavelengths of the order of 10 cm, synchrotron radiation is 
dominant; given the numbers and energies of the electrons which 
emit the galactic synchrotron radiation, it is possible to deduce 
the strength of the general magnetic field of the Galaxy, Un- 
fortunately, the data for the numbers and energies of the electrons 
are not known accurately, and various assumptions have to be 



77 



made. Since high-energy electrons are responsible for the syn- 
chrotron radiation, it is logical to suppose that their characteristics 
are much the same as for cosmic ray particles (or. more properly, 
the electronic component of cosmic radiation). If so. the strength of 
the interstellar magnetic field must be approximately I x 10 _G gauss. 

Faraday rotation 

The propagation of electromagnetic radiation in the Galaxy is 
affected by the general galactic magnetic field. Consider, for 
instance, a polarised electromagnetic wave with a propagation 
along the direction of the magnetic field. A linearly-polarised wave 
has its own electric field, which, at any set point in space, vibrates 
in a plane agreeing with its direction ol" motion ; that is to say, its 
plane of polarisation. During its movement, however, it is affected 
by the spiralling of the electrons in the magnetic field, and the plane 
of polarisation will rotate progressively, causing what is termed the 
Faraday effect. Obviously, the Faraday effect wiil depend upon the 
strength of the magnetic field, the electron density, and the distance 
covered by the wave. 

Table 2 gives the values for the rotation of the plane of polarisa- 
tion, expressed in degrees, for a magnetic field of 10 -8 gauss, an 
electron density of 0* 1 electron per cubic centimetre, and a path- 
length of 3-26 light-years. (This distance - 3-26 light-years is also 
known technically as one parsec.) 

Measurements of the directional differences of the planes of 
polarisation for different wavelengths, from extragalactic radio 
sources, give some idea of the strength of the magnetic field of the 
Galaxy, provided that the electron density is known. These measures 
indicate that the magnetic field is greater lhan 2 X 10~ 6 gauss. 



Radio sources and cosmic radiation 

It has been shown that most of the non-thermal radio radiation 
from the Galaxy comes from discrete sources, and that it is due to 



78 



33 The Crab Nebula. Ml. photographed in colour with the 200- in. Hale 
reflector at Palornar. This Nebula is the remnant of the supernova observed in 
■) 054 by Chinese and Japanese astronomers. Its distance is 4,000 light-years and 
the gases are still expanding outwards from the explosion- centre. The Crab 
Nebula is a source of radio emission and X- radiation and is one of the most 
significant objects in the Galaxy. Nothing else quite like it is known. 



the movement of high-energy electrons in a magnetic field; there 
are various means of estimating the strength of the galactic 
magnetic field, and it has also been noted that cosmic radiation is 
spread all through the Galaxy. 

The presence of high-energy electrons in galactic radio sources, 
such as the Crab Nebula, indicates that these sources contain 
protons and other high-energy nuclei, and that the sources arc 
responsible for sending out the cosmic ray particles. In other words, 
there is a close connection between cosmic rays and non-thermal 
radio sources. The mechanism of cosmic-ray production will 
therefore be better understood when the conditions inside the non- 
thermal radio sources have been determined. 

In the Crab Nebula, for instance, the number of high-energy 
electrons must be about 1 per litre; their energy is of the order of 
10 12 electron volts, and they radiate in a magnetic field of about 
I x 10 -8 gauss. Such electrons must lose all their energy in a few 
decades; the energy will have been radiated away. Yet the Crab 
Nebula has certainly existed for more than 900 years (remember 
that the supernova responsible for it was watched as long ago as 
the year 1054). High-energy electrons must be continuously re- 
plenished, and so the appropriate energy-sources must be active 
all the lime. Such energy-sources are easily found. High-energy 
protons collide with slow electrons; these electrons are speeded up, 
and it is the accelerated, now fast-moving electrons which are 
responsible for the non-thermal radiation. 

There are great differences between protons and electrons. The 
high-energy protons can last for much longer than the electrons 
because they lose no energy through radiation and very little by 
collision. The energy spectra of the electrons produced by collisions 
with the protons of high energy is a faithful representation of the 
energy spectra of the protons themselves. 

It might therefore be supposed that all supernova explosions are 
likely to produce cosmic radiation. If so, then from time to lime 
(perhaps once per century) a fresh supernova outburst will inject a 
further supply of cosmic ray particles into the Galaxy. Part of this 




80 



81 



radiation would escape into intcrgalactic space; braking would 
account for the loss of another pari, and the rest would receive 
extra acceleration wilhin the Galaxy. The composition, intensity and 
energy of cosmic radiation, as observed from the Earth, seem to be 
in substantial agreement with this idea. 

Conclusion 

Following a description of the observational methods and results, 
it may be useful to draw up a balance-sheet, if only to put all these 
ideas into their proper perspective. First there is the question of 
distance and here, an everyday comparison will be of help. A ten- 
centimes coin placed under the Arc dc Triomphc, in Paris, will 
subtend an angle of 1 second of arc as seen from the Carrousel 
(Tuileries). The ratio between the diameter of the coin and the 
distance between the Arc de Triomphe and the Carrousel is very 
nearly the same as the ratio between the radius of the Earth's orbit 
round the Sun, and the distance of Proxima Centauri, the nearest 
star. The Sun is 1 1,000 terrestrial diameters away; the nearest star 
is 250,000 limes more distani than ihe Sun; the distance from the 
Sun to the centre of the Galaxy is about 10,000 times the distance 
between ourselves and Proxima Centauri. 

Much depends upon what is meant by the terms 'near' and 'far'. 
Inside the Solar System, "near the Earth' means a few million 
kilometres; with respect to the slars, 'near the Sun* means a few 
light-years. Stars which are some thousands of light-years away are 
said to be 'distant', bul, as will be described later, a 'near' galaxy is 
situated at a distance of millions of light-years. 

There is also ihe question of the time-lag between the moment 
when the light is emitted by a star and the moment when we see it. 
For instance, a nova 2,000 light-years away will have suffered its 
actual outburst 2.000 years before we see it. From a scientific point 
of view, however, this does not matter in the least; there is no need 
to know the exact dale of any particular event of this kind. With 
individual stars, it is the chronological sequence of events which is 






important, and whether the events began 10, 100 or 1 ,000 years ago 
is of little consequence. With large groups of stars, statistical 
methods take over, and any effects due to the time-lag disappear. 
Moreover, the delays are insignificant with respect to the evolution 
of a star or galaxy. It is quite true thai there are some dynamical 
effects, because the stars are never where we see them; ihey have 
moved on in their paths since they emitted the light now reaching 
us, and yet, taken as a whole, ihe Galaxy is evolving so slowly that 
effects of this kind are really not important. 

The Earth moves round the Sun, and the radius of its orbit is 
the basis of all distance-determinations. The Sun itself is a star with 
no particular noteworthy characteristics; it moves in a somewhat 
eccentric orbit round the centre of the Galaxy, taking 250.000.000 
years to complete one journey. At present its distance from the 
galactic centre is about 30,000 light-years. 

Around us are the other stars of the Galaxy, and between them 
there lies nebulous material composed of gas and dust. It is known 
that one-third of the galactic mass is contained in the visible stars, 
while one-sixth of it appears as nebulous material. There remains 
a mass equal to about one-half of the total, about which nothing 
certain is known. 

There are about 100,000 million stars in the Galaxy; they may be 
divided into two different 'populations', and the movements of 
these two groups may be distinguished. Also, the distribution of the 
stars in the Galaxy is associated with their types of movements. The 
Galaxy is flattened in shape, because it is in a state of rotation, and 
because of the way in which the different groups of stars are spread 
out above and below the main plane of the system. And just as the 
two definite stellar populations differ in movement, so also the stars 
in them differ physically. 

The galactic gas. like the stars, is made up essentially of hydro- 
gen, which is the principal constituent of the universe. This 
interstellar gas carries with it magnetic fields, which may be 
detected because they cause the polarisation of starlight and the 
rotation of the plane of polarisation of radio waves. The magnetic 



r 



34 Positions of the X-ray sources detected by Bowyet, Chubb 
and Ffiedmann by means of detectors flown in rockets. The 
numbers indicate the probable identities: 1 Crab Nebula: 
2, 3, and 4 sources in Scorpio; 5 Kepler's supernova in Ophiuchus. 
seen in the year 1 604 ; 6 galactic centre in Sagittarius ; 7 source 
in Sagittarius ; 8 source in Serpens ; 9 source in Cygnus. 



northern Hemj sp /, e/ . e 










83 



so utf>ern Hemisph^ 




84 



field has a structure which is both complex and turbulent, and it 
controls the movements of the particles of galactic radiation. The 
gas itself lias an average density of about three hydrogen atoms per 
cubic centimetre, which works out at about one solar mass per 
cubic light-year. To this we must add the stars, which account for 
about two solar masses per cubic light-year. About one particle out 
of 10.000 million is a cosmic-ray particle, and there is one grain of 
dust Tor every 10.000.000,000,000 atoms of hydrogen. 

Of course, astronomers arc familiar with all these numbers, and 
have little difficulty in understanding their significance. To draw up 
an accurate picture of the Galaxy as a whole, and to understand the 
relative crowding of what is so often called 'empty space', it is 
essential to took at things from a distance. 



3 Time 



85 



The universe evolves in time, and therefore we need a chronology 
which must be as exact as possible, bearing in mind that we have to 
dual with periods of tremendous length. 



Time in the mechanical sense 

Studies of the motions of bodies are based upon relationships 
between time, the forces concerned, and the amount of space 
involved. To begin with, the principle of inertia, laid down origin- 
ally by Galileo, states that a moving body will cover equal distances 
in equal times, in the absence of any external applied force. Of 
course, this state of affairs - the absence of external force - is 
never encountered in the universe. It represents an ideal of classical 
mechanics, but it can never occur. However, the rotation of the 
Earth on its axis provides a fairly close approximation, if the 
Earth were a perfectly rigid sphere, all the forces acting upon it 
would be exactly balanced; its rotation, due solely to inertia, would 
be absolutely uniform, and it would rotate through 1/86,400 of its 
circumference in a period of one second of lime. 

This, needless to say, does not happen. Twenty years ago it was 
found that the length of the "day' is not constant, and in 1950 
astronomers agreed to define the "second' as a fraction of the 
year 1900. It was assumed that 1900 lasted for 31.556.925-9747 
seconds, and this value is regarded as reliable, so that it serves 
as a standard for the future. Yet we cannot be sure that this 
is precisely the same as mechanical time, and so it has been given 
the name of Ephemeris Time. 

Having defined the second as a definite fraction of the year, the 
notions of acceleration and force follow. Acceleration expresses the 
change in velocity with time. With bodies falling freely, the velocity 
increases by equal amounts in equal time-intervals, and this is, of 
course, the acceleration. At the Earth's surface, the acceleration due 
to gravity is 9-81 metres per second, so that in free fall a body will 
increase its velocity by 9-81 metres per second in each second. 

The acceleration of movement is due to a force which acts on the 



86 



body. This force is proportional to the acceleration, and the 
constant of proportionality is the mass usually known as the 
ineriial mass, since it is the inertia of the mass which acts in 
opposition to the motion. With uniform circular motion, the 
velocity changes direction continuously, because it must remain 
tangential to (he circle. An instantaneous change in direction will 
therefore cause an acceleration toward the centre of the circle, 
often called the centrifugal acceleration. With a planet moving 
round the Sun, the acceleration due to its orbital motion is equal 
to the acceleration caused by the Sun's attraction, so that the 
al tractive force is proportional to the weight mass, that is, the 
mass as attracted by the Sun. In classical mechanics, as in relativity, 
inertial mass and weight mass are regarded as identical. 

Time in the mechanical sense depends both upon acceleration 
and upon the force of attraction. This is easily seen by considering 
the behaviour of a pendulum clock, in which the swing of the 
pendulum is controlled by the Earth's gravitational pull; this force 
must therefore be taken into account when defining the period or 
the swing. 

Gravitational forces are responsible for the motions of all the 
bodies in the universe, and the equivalence of gravity and accelera- 
tion is clearly shown. And since 'time' must be included in any 
definition of acceleration, the verification of the laws of motion 
means that mechanical lime must be the same for the movement 
of the Earth round the Sun, the movements of stars in our Galaxy, 
and for the movements of stars in other galaxies. 



Time and energy 

There are various forms of energy, such as the kinetic energy due 
to motion, potential energy in a gravitational field, radiant energy, 
i he energy due to thermal agitation of molecules of a gas, and the 
internal energy of an atom. Experience proves that these different 
forms of energy can be transformed from one to another. The law 
of the conservation of energy is fundamental in physics. 



87 



The transformation of energy is never instantaneous; it takes a 
certain period of lime. For any system, it is possible to define the 
quantity of energy which is transformed, in unit time, into another 
energy-form. The quantity of energy per unit of time is known as 
the power. Horse-power is « very common unit; the official unit 
is the watt. In a hydro-electric installation, lor example, energy is 
in reserve behind the dam in the form of potential energy; in the 
flow pipes, it is changed into kinetic energy: and when the kinetic 
energy of the moving water turns the rotors of the dynamos, the 
result is a change into electrical energy. The quantity of electrical 
energy which enters the grid per second is equal to the power 
available in each second of time at the highest water-level in the 
system locked up in the form or potential energy - taking into 
account, of course, the inevitable losses due to such causes as rises 
in the temperature of the water, kinetic energy of the dynamo 
rotors, and the energy wasted upon the low-level water flowing out 
of the system. 

When the capacity of the system is known, together with the 
amount of potential energy held in reserve behind the dam. it is 
not difficult to calculate the period during which the system can be 
supplied without the need for providing extra water behind the 
dam. Since energy is the produce of power by time, it is clear that 
each release of energy must lake a certain time, and the relationship 
between time, energy and power may be considered as a novel 
way of defining "time'. 



Time and light 

Light is a vibratory phenomenon, and the unit of lime can therefore 
be defined as ihe period necessary to complete a set number of 
vibrations. Visible light presents difficulties, because the frequency 
is so high lhat the periods of vibration are much too short lo be 
measured by conventional means, but oscillations in what is 
termed the radio range can be linked with a timekeeping device, 
producing what is known as an atomic clock. When an atom 



88 



Table 3 


Composition 


of some atomic nuclei 




Nucleus 


Number of 


Number of 


Atomic 


Mass 




neutrons 


protons 


number 


number 


Neutron 


1 








1 


Proton 





1 


1 


1 


Helium (in 










(i-panicle) 


2 


2 


2 


4 


Carbon 


6 


6 


6 


12 


Oxygen 


8 


8 


8 


16 


Potassium 


21 


18 


18 


39 


Potassium 


22 


18 


18 


40 


Potassium 


23 


18 


18 


41 


Rhenium 


110 


75 


75 


185 


Rhenium 


112 


75 


75 


187 


Osmium 


108 


76 


76 


184 


Osmium 


110 


76 


76 


186 


Osmium 


111 


76 


76 


187 


Osmium 


112 


76 


76 


188 


Osmium 


113 


76 


76 


189 


Osmium 


114 


76 


76 


190 


Osmium 


116 


76 


76 


192 


Uranium 


142 


92 


92 


234 


Uranium 


143 


92 


92 


235 


Uranium 


146 


92 


92 


238 



89 



changes from one energy-state to another, it emits or absorbs 
radiation at radio wavelengths. An emitter is tuned to the fre- 
quency concerned, and the atoms are so constant in their behaviour 
that the clock is extremely accurate. Using a stabilised radio 
frequency, the clock itself, which uses a mechanical system, can he 
controlled and read. 

One element particularly useful in this respect is cssium. The 
csesium clock, using 3-18-centimetre radio waves, is so precise that 
the old definition of the 'second* has been replaced by a new one, 
dependant upon the frequency of caesium. In fact, mechanical time 
has been superseded by electromagnetic time. 

Time and the atom 

When an atom or an atomic nucleus is in an excited stale, it will 
eventually fall back naturally to a lower slate of excitation. With 
an atom this process is accompanied by the emission of light ; when 
an atomic nucleus is involved, the process involves various pheno- 
mena which go under the general name of radioactivity. 

Radioactivity 

An atomic nucleus consists of two different kinds of particles, 
neutrons and protons, whose masses are almost equal. The atomic 
number of the element depends upon the number of protons, equal 
to the positive electrical charge of the nucleus. The total number of 
particles gives the mass number. Some typical examples are given 
in table 3. 

The number of electrons moving round the nucleus is equal to the 
number of protons in the nucleus. The number of electrons de- 
termines the chemical properties of the atom; and since atoms are 
identified by means of their chemical properties, the atomic 
number fixes the chemical species. When a given chemical species 
exists with atoms of different mass numbers, the term isotope is 
introduced, and both chemical name and mass number of the 






90 



91 







Table 4 


Number of radioactive nuclei 


Number 


Time 


N 





N/2 


T 


N/4 


2T 


N/8 


3T 



atom have to be given in identification. Thus uranium-234 and 
uranium-238 arc isotopes of the same element, uranium. 

A radioactive atom, such as uranium-238, disintegrates spon- 
taneously with the emission of a helium nucleus (alpha-particle). 
giving a species of a different element, thorium. It is transformation 
of this kind which is called radioactivity. At the end of a long and 
complicated series of transformations, uranium-238 becomes 
lead-200. Lead- 200 is stable, and does not disintegrate further. 
Similarly, a radioactive nucleus of rhenium- 187 disintegrates 
spontaneously and emits an electron, becoming osmium- 187; this 
process is known as beta-radioactivity. Further details will be 
given later. 

Not all the nuclei in a given group suffer radioactive disintegra- 
tion at the same moment. In a group of N nuclei, a certain number 
(N/P) will undergo transformation in one second, P being the lime 
concerned. The quantity (l/P) is known as the constant of radio- 
activity. At the end of a certain time T. the number of unaffected 
nuclei will have been halved; this period, T, is the half-life. The 
numbers of remaining nuclei after periods of T, 2T» etc.. are given 
in table 4. The decrease in number follows a geometrical pro- 
gression. If it is possible to determine the number N, at a time ti. 






and the corresponding N2 and tg, and if the radioactive period is 
also known, the time interval h ti follows. Radioactive periods 
can be measured in the laboratory; the time interval ta — ti is then 
called the time of radioactivity. 

Important problems are raised by the different methods of mea- 
suring the time intervals. Each method is based on a different set of 
phenomena, and each requires a different set of physical constants. 
It may be asked whether the student should assume the essential 
identity of mechanical time, energy time, electromagnetic time, and 
radioactive time. In the following discussion this identity will be 
assumed; but later in this book, under the heading of cosmology, 
it will be necessary to deal with theories based on the idea that 
mechanical time and radioactive time lead to different results with 
regard to the course of evolution of the universe as a whole. 



Cosmical chronology 

In any cosmological discussion, it is necessary to date past events 
as accurately as possible. In principle, a chronology can be drawn 
up for any evolutionary process; all that is needed is a knowledge 
of the laws which control it, together with information about the 
state of affairs at a "starting point' from which the evolution is to 
be tracked. If it is possible to fix the dates of the origin of the Earth, 
the formation of the radioactive elements, the origin of the Galaxy 
and of the main groups of stars, we shall have a firm basis from 
which to work. 



The age of the Earth 

There are various methods for measuring the age of the Earth, but 
of these probably the best depends upon the process of radioactive 
decay. There are three principal families of radioactive elements: 
those of uranium-238, uranium-235 and thorium-232. Each ends 
its career as some species of lead, as follows: 



92 



Uranium-238: 
Uranium-235: 
Thorium-232: 



■* lead-206 
-* lead-207 
-* lead-208 



All these three stable isotopes of lead are known to occur naturally. 
Therefore, however the elements were formed, there must be some 
natural lead which has been produced by the decay of radioactive 
uranium and thorium. 

Of course, the original quantities of lead-206. 207 and 208 are not 
known, but the problem can be solved by examining rocks of 
different ages. These rocks were formed from a magma, and have 
retained the lead isotopes which have been produced throughout 
the Earth's history by the decay of uranium and thorium. In any- 
given rock, the relative abundance of this lead depends partly upon 
the initial quantity of uranium or thorium, and partly upon the 
age of the rock. By using rocks of known age as reference stan- 
dards, the ages of the lead-containing rocks may be deduced. Of 
course, the Earth itself must be older than the oldest rocks, but 
such differences are minor when such immense spans of time are 
being considered. By the radioactive-decay method, the age of the 
Earth works out at about 4,600 million years. 

When meteorites are studied in the same way, the results are of 
the same order, so that presumably the Earth and the meteorites 
were formed at roughly the same epoch. From this, it is only one 
step more to derive an estimated age for the Solar System, and so 
providing the first and one of the most important dates in our 
'cosmical chronology*. Irrespective of the method employed, it 
would be absurd to derive an age for the Galaxy or the universe 
which is less than the known age of the Earth and Solar System! 

The age of the radioactive elements 

It is easier, and more straightforward, to determine the age of 
radioactive elements. Since they virtually disappear in the course of 
time, they cannot have existed for an indefinite period in the past. 



93 



The Solar System, presumably formed from interstellar gas, gives 
information about the composition of this gas 4,600 million years 
ago. During the previous period, that is. from the formation of the 
Galaxy to the formation of the Solar System, radioactive elements 
had been produced, and were scattered throughout the interstellar 
gas. They can be accounted for only by one particular event 
(presumably unique), or else by a succession of events taking place 
in the Galaxy. 

If it were possible to find out the relative abundances of two 
types of nuclei at the time of their original formation, then the 
present-day relative amounts would tell either the date of the 
original sole event or else the time during which the formative 
processes have been going on, whichever case is relevant. Of course, 
this information cannot be found from observation, and to decide 
upon the original relative abundances it is necessary to rely upon 
theory. To show the general nature of the investigation, it may be 
best to take one particular example. 

Let us consider the decay of rhenium- 187 into osmium-187, by 
the beta process (that is to say, by the emission of a beta-particle. 
which is nothing more nor less than an electron). The half-life of 
rhenium-187 is 4,500 million years. Starting from the present-day 
relative abundances of rhenium-187 and the two osmium isotopes, 
it is possible to calculate the abundance ratio of osmium-187/ 
rhenium-187 at the time of the origin of the Solar System. The 
relative abundance is due entirely to the decay of rhenium-187. 
If we are dealing with a single unique event, its time must be put 
back about 6,000 million years before the formation of the Solar 
System : if a succession of events is preferred, all of the same kind 
and each producing radioactive elements, the total period involved 
must be something like 13,000 million years before the Solar 
System came into being. 

In fact, it seems that the radioactive elements in the Galaxy 
were produced at some time between 11,000 million and 18,000 
million years ago. Studies of the lead produced by uranium-238 
and uranium-235 yield a similar figure. It is reasonable to suppose. 



94 



35 Cluster NGC 2632. In the central region of the cluster 
there is a 'nucleus' consisting of a quadruple star of the 
trapezium type, with its lour components at much the same 
distance from each other. Ambartsumian has shown thai 
these multiple stars are highly unstable and so must be 
young - a result confirmed by other studies of stellar evolution. 



95 



ihcn, lhal the radioactive elements came into existence not long 
after the Galaxy itself, so that by studying them we are also studying 
the earliest part of galactic history. 

Stellar energy 

Stars radiate energy, and continue to shine because they are 
drawing upon the energy-reserves locked up in the nuclei of their 
constituent atoms. Not all stars radiate by identical processes, but 
the general principles involved are much the same. 

The Main Sequence stars, described earlier, burn their hydrogen 
in a Tusion reaction in which four hydrogen nuclei produce one 
nucleus of helium: 



4 (hydrogen- 1) 



1 (helium-4). 



The amount of energy released each time one gram of hydrogen 
is changed into helium amounts to 630,000 million joules. This 
enormous energy is of the same kind as that which modern 
scientists hope to make available by peaceful development of 
nuctear power; the stars are natural centres of controlled fusion, 
but their energy reserves are not inexhaustible. No star can 
transform more hydrogen than it contains. 

It may be useful to go back to the analogy of the dam. described 
on page 87. A hydro-electric station can continue to produce power 
so long as water is stored up behind the dam, and similarly it may 
be said that a star continues to shine so long as it has enough stored 
energy. If the total amount of energy being sent out is known, and 
also the quantity of stored energy, it is possible to calculate how 
long the star can go on radiating. 

Hydrogen makes up about 80 per cent of the Sun's mass, and 
this is enough to allow the present output of radiation to continue 
for about 10.000 million years in the future, provided that all the 
hydrogen is regarded as available for use. A star which is more 
luminous than the Sun will squander its energy reserves at a faster 
rate, and a very hot, blue star can hardly keep on shining with its 




36 A colour - mag n it u d e d i agra m f or va rious 
star- clusters. The youngest clusters, such as 
NGC 2632. show a long Main Sequence, 
With an old cluster, such as M67. the 
upper part of the Mam Sequence is missing. 



-8 



-6 



-4 



-2 



M v 



"i r 

NGC 2362 



I age year | 
VOX 10 s . 

20x10 6 _ 



6 _ 



8 1 L 



-4 




97 



present brightness lor more than about 10.000,000 years. However, 
these figures give no information about stellar evolution : neither do 
they lead to a reliable date for the origin of the stars concerned. 



Stellar evolution 

With stars, intrinsic luminosity increases rapidly with increasing 
mass. The amount of energy produced by a gram of material is 
greater in the cases of more massive stars, and this in turn speeds 
up the rate of evolution. Lone stars are not very informative, but 
much can be learned from star-clusters, in which the individual 
members are linked by gravitation into a definite system. 

It is virtually certain that the stars in a cluster have a common 
origin, and are of about the same age, but the masses of the 
individual stars differ, and the most massive stars have evolved the 
most rapidly. In fact, a cluster offers us a sort of picture of stellar 
evolution. The best means of investigation is to measure the colour 
indexes and luminosities or individual stars. When colour index is 
plotted on the horizontal axis against luminosity on the vertical 
axis, it is clear that the distribution is not random; each cluster 
yields a definite pattern, and theoretical work on the colour- 
luminosity diagram has led to a satisfactory knowledge of the way 
in which a star slowly evolves along the Main Sequence. 

When stars are formed, the hot gas from which they originate has 
been subject to violent convection currents. At this stage, a star has 
the same composition throughout its globe, with the same pro- 
portions of hydrogen, helium and other elements all the way from 
surface to centre. When the hydrogen-into-helium process begins, 
it can do so only where the temperature is greatest; that is to say. 
near the centre of the star. In most stars, there is no thorough 
mixing of the material, and it is the central regions which change, 
altering their composition and structure as the amount of hydrogen 
becomes less and less and the relative quantity of helium becomes 
greater and greater. The effects at the star's surface remain imper- 
ceptible over long periods of time; but when about 10 per cent of 



37 A visual colour magnitude for the cluster NGC 1 88 together 
with field stars not associated with the cluster. The almost 
straight line marks the Main Sequence ; the curved line 
represents the stars of NGC 1 88. The position of the field 
stars, which are usually closer to us than the cluster, indicates 
that they are youngenhan the cluster stars. 



— o 




I 


I . I 

■ 
* 


1 

• 

• 


1 

• • 




-4 






• 
• 

• • 


I 

• 


• 




-2 






• 

• 
* 

• 


* 

• • 

r 'Si 






















A 






. WMTT/ . 




















2 








• 




^^ 


4 






w * * /J 








6 














8 




I 


1 X 


1 


1 





8 1-2 

(B-V) 



16 



20 



99 



Table 5 Ages of 


some star clusters 


Cluster 


Age in years 


Ursa Major 


300 million 


Hyades 


800 million 


NGC2158 


800 million 


NGC 752 


1.000 million 


M67 


9,000 million 


NGC 188 


14,000 million 







the hydrogen has been changed into helium, the star's radius and 
luminosity start lo increase. The star becomes redder, so that its 
colour index increases, and the star itself moves toward the upper 
right of the colour/luminosity diagram. 

On the diagram, it is possible to calculate theoretical curves of 
equal age. known as ixochrones; it is found that these agree excellent- 
ly with the curves drawn up by observation. Simply by examining 
the curves, the age of the cluster can then be deduced. Various 
clusters have been studied in this way, and some of the results are 
given in table 5. Of course, the clusters are not all of the same 
density; that known as the Ursa Major cluster is very scattered, 
while others, such as NGC 752, are considerably richer. As has 
been noted. NGC stands for Dreyer's New General Catalogue of 
clusters and nebula; M is the number of the cluster in Messier's 
catalogue of the eighteenth century. 



The ages of the stars in the Galaxy 

Empirical isochrones sweep the colour/luminosity diagram from 
left to right. Therefore, it seems safe to say that in general, stars 
which lie to the left of any given isochrone are younger than stars 
which are situated on the isochrone. 



100 



In ihis respect, (lie cluster NGC 188 is particularly significant. If 
stars in the neighbourhood of the Sun are put in on a diagram 
representing the stars of NGC 188. it is found that alt of them tie 
to the left of the NGC 188 branch. It seems reasonable to suppose, 
then, that NGC 188 is the oldest known cluster in the Galaxy; and 
if the Galaxy is older still, as presumably it must be, then its age 
cannot be much more than that of the cluster. 



The evolution of the Galaxy 

The stars in our Galaxy are evolving, but so is the Galaxy itself. 
The next problem is to see what are the indications of this evolution, 
and how it affects the careers of the individual stars. The essential 
clues are provided by three facts, based on observation : 

1 Stars evolve, and change their chemical composition, by means 
of nuclear reactions inside their globes. 

2 Stars eject part of their material into the Galaxy sometimes 
rapidly, sometimes slowly and so modify the chemical composi- 
tion of the interstellar matter. 

3 Within the Galaxy, fresh stars are continually being produced 
from the interstellar material. This is demonstrated by the close 
association between the vast interstellar clouds and the youngest 
known star-clusters. 

This latter point means that recently-born stars, produced from 
the modified interstellar matter, are of different chemical composi- 
tion from the old stars. To see just how this process works, it is 
necessary to look more closely at the nuclear reactions in stellar 
interiors. The technical term for this is nucleosynthesis. 



Nucleosynthesis 

To give a complete description of the nuclear processes going on 
inside the stars would be beyond the scope of this book, but the 
essential stages must be noted. First, the temperature of the central 
regions of a star rises progressively as the star evolves. It is import- 



101 



Table6 Nuclear reactions 
Temperature (°C) Reaction 

20.000.000 4 (hydrogen-1) 



helium-4 



1 00,000.000 io 200,000.000 3 ( helium-4) - carbon-1 2 

carbon-1 2 + helium-4 — oxygen 1 6 
oxygen- 1 6 + helium-4 — — neon-20 



3.000,000,000 



Formal ion of iron al equilibrium 



ant to remember that reactions between atomic nuclei can become 
very rapid only when the temperature is high enough, and that the 
nuclear reactions within the star must be completed in definite 
phases of the star's evolution. 

The first stage, already described, is the transformation of 
hydrogen into helium, so producing a core of helium at the star's 
centre. As the evolution proceeds, and the central temperature 
rises still more, new reactions take place in the helium core. The 
first of these is the transformation of helium into carbon, with the 
emission of very shorl-wavelenglh radiation known as gamma- 
radiation: 

3 (hclium-4) »■ 1 (carbon- 12) + gamma-radiation. 

This is followed by the transformation of carbon into oxygen and 
of oxygen into neon, with emission of gamma-rays: 

carbon-12 + helium-4 * oxygen-16 + gamma-radiation 

oxygen- 16 + helium-4 ► neon -20 + gamma-radiation. 

A further increase in temperature alters the whole situation. 
Instead of irreversible reactions of the kind already met with, the 
processes become more numerous and varied; they take place so 
rapidly that the direct and inverse processes occur equally between 



102 



the various kinds of nuclei, resulting in a stale of equilibrium. Under 
these conditions, the nuclei which appear are those which are of a 
particularly stable kind: iron and its neighbours in the table of 
elements - titanium, vanadium, chromium, manganese, cobalt and 
nickel. The scale of temperatures is given in table 6. 

Equilibrium conditions inside a star can be attained only when 
the star has reached an extreme state of contraction. For these 
conditions to occur in the Sun, for instance, the solar radius would 
have to shrink to only 1/100 of its present value; otherwise, the 
central temperature would not be high enough. Certainly an event 
of such a kind would be catastrophic. No star could maintain this 
temperature for very long, simply because the nuclear reactions 
then take place so quickly. Yet such catastrophes can be observed 
in nature: we call them the explosions of supernova;. 

Supernovae 

Occasionally, very powerful explosions occur in our or other 
galaxies; a formerly faint star suffers a tremendous outburst, and 
blows much of its material away into space, releasing enormous 
quantities of energy. It is true that few supernovas have been seen 
in our Galaxy; the most celebrated are those of 1054, which 
produced the Crab Nebula, and two of later date, Tycho's star 
(1572) and Kepler's star (1604). However, many others have been 
observed in outer galaxies, and their general properties are reason- 
ably well known. 

At maximum, the absolute magnitude of a supernova may reach 
— 20. so that it is then as brilliant as an entire galaxy. Studies of the 
way in which supernova; vary in brightness after the initial outburst 
have shown that there arc two definite types. Supernova; of Type 

I decrease slowly in brightness after maximum; they are most often 
seen in elliptical galaxies and in the central parts of spirals. Type 

I I supernova; fall rapidly from maximum brightness, and tend to 
occur most commonly in the spiral arms of galaxies. It is estimated 
that in each galaxy, an average of three to four supernova; is seen 



103 



per thousand years, so that a supernova is a relatively rare 

phenomenon. 

The total quantity of energy set free in a supernova explosion is 
enormous; it corresponds to the total energy radiated by the Sun 
over a period ofabout 10,000 million years. For a mass equal to that 
of the Sun. this corresponds to about half a million electron volts 
per nucleon. Only nuclear reactions can provide energy-sources of 
this order. Also, the rapidity of the explosion means that the 
energy is released suddenly; since reaction-speeds increase with 
temperature, it seems that there must be a tremendous rise in 
temperature just before the outburst. It is true that the contraction 
of a star is accompanied by an increase in the temperature near the 
core, but with a supernova the contraction would have to be very 
rapid as rapid, indeed, as the nuclear reactions themselves. This 
appears to be due to a collapse of the layers of the star under their 
own weight, so that, broadly speaking, a supernova outburst is 
caused by the gravitational collapse of a star. 



Formation of the heavy elements — the neutron 

Whether or not the star suffers a final catastrophic outburst, and 
becomes a supernova, there are various other reactions which can 
take place at rather lower temperatures. These involve neutrons 
and beta-rays. 

A neutron is a particle without an electric charge and with a 
mass slightly greater than that of a proton; taking the oxygen 
nucleus to have a mass of 16, with a hydrogen nucleus having a 
mass of 1 '00812, the value for the neutron is 1-00893. It decays 
spontaneously, yielding a proton, an electron, and a mysterious 
particle called a neutrino, which has no mass and which will be 
described below. The process is: 

Neutron (I) * hydrogen-] + electron + neutrino. 

The neutron, whose half-life is 12 minutes, was discovered in 1931 
by F.Joliot and I. Curie, who were studying the penetrative radia- 



104 



tion emitted when beryllium is bombarded by helium nuclei (alpha 
particles) according to the following reaction: 



Beryllium-9 4- helium-4 



carbon- 12 -f neutron 1. 



A nucleus of atomic number Z and mass number A can easily 
capture a neutron, to form an isotope of the same atomic number 
and mass number A+l. The simplest example of this, originally 
found in 1934. is that of a neutron being captured by a proton, 
forming a nucleus of deuterium ('heavy hydrogen') with the 
emission of gamma-radiation : 



Hydrogen- 1 + neutron 1 



* deuterium 2 + gamma- 
radiation. 



Beta- radioactivity and the neutrino 

Some nuclei are stable, while others are unstable. If an isotope is 
heavy, that is to say. rich in neutrons, or light and therefore poor in 
neutrons, it is unstable, and changes spontaneously into a stable 
nucleus. If heavy, the process will be accompanied by the emission 
of a negative electron. If the nucleus is light, it will either emit a 
positive electron or capture a negative one. 

This beta-radioactivity is remarkable in that the emitted electron 
may have any quantity of energy between zero and the maximum 
amount available in the transformation concerned. At first sight, 
this seems to contradict the law of the conservation of energy, 
and so in 1931 the famous physicist Pauti postulated the existence 
of an uncharged particle (to account for the fact that the total 
charge in the transformation was not affected) of very slight mass 
(to explain why it had not been observed). Another eminent 
physicist, Fermi, named this particle the neutrino. Since then, of 
course, its existence has been confirmed. 

All fundamental particles show axial rotation, and each particle 
has its own "mirror image* or anti-particle. For instance, the 
positive electron, or positron, is the opposite of the familiar nega- 



105 



tive electron; the positive proton is balanced by a negatively- 
charged anti-proton, discovered at Berkeley in 1955; and similarly, 
the 'mirror image* of the neutrino is the anti-neutrino. In beta- 
radioactivity, the emission of a negative electron is accompanied by 
the emission of an anti-neutrino; the capture of a negative electron 
goes together with the emission of a neutrino, while the emission of 
a positive electron involves also the emission of a neutrino. 

The capture of a neutrino by matter is very difficult, and this has 
made it far from easy to obtain experimental evidence for the 
neutrino. However, final proof was forthcoming in 1955. from 
workers at Los Alamos. The nuclear reactions in the pile of the 
Savannah River atomic station release very large numbers of anti- 
neutrinos, and these are carried through a water reservoir, so 
that a few of them are captured by hydrogen nuclei: 



Proton + anti-neutrino ■ 



► neutron + positive electron. 

Cadmium salts dispersed through the water allow the neutrons to 
be detected. The cadmium isotope which is formed becomes 
excited, and emits gamma radiation: 



neutron 1 + cadmium 



excited cadmium- 



cadmium + gamma-radiation. 

The positive electron is captured by the negative electrons of the 
water, and two gamma rays are emitted. Counts were possible by 
means of the simultaneous detection of gamma-rays from the 
cadmium and the positive electron. The reactions took place at the 
rate of three per hour in the 500 litres of water used in the 
experiment. 

The neutrino is so difficult to capture that to ensure its absorption 
by the hydrogen nuclei in the water, it would have to be sent 
through a column of water 250 light-years long! This properly of 
the neutrino, the fact that its capture is practically impossible, 
means that it can travel for immense distances without being 
halted. This is of great cosmological interest. 



106 



107 



Capture of slow neutrons 

In the capture of slow neutrons, a radioactive nucleus is produced, 
and beta-emission follows. These slow neutrons are, therefore, 
always captured by stable nuclei. Starting from neon, or, more 
appropriately, with iron, which is relatively plentiful in an average 
star, nuclei of successively greater mass numbers can be built up. 
In the course of successive captures of neutrons, the nuclei which 
find the greatest difficulty in capturing neutrons become more 
plentiful, because they arc more easily formed than disrupted. 
This applies to nuclei with 14, 20, 28, 82 and 126 neutrons (see 
table 7). 

Neutrons are produced when the temperature rises because of 
the action of radiation upon neon. The reaction is as follows, and 
involves an absorption of 17,000,000 electron volts: 



Table 7 Stable elements 



->■ neon- 1 9 + neutron. 



Neon -20 + gamma-radiation — 

Neon- 19 is transformed by beta-radioactivity, and becomes 
fluorine. When ihc temperature rises above several hundred 
million degrees, the numbers of high-energy photons become 
great enough to release a few hundred neutrons per atom of iron 
over a period of a few thousands of years. 



Capture of fast neutrons 

At slightly higher temperatures, the iron may be irradiated in a 
few seconds by an enormous flux of neutrons. The process is so 
rapid thai it must necessarily occur in the region of the gravitational 
catastrophe which results in a supernova explosion. There is simply 
not enough time between two successive captures of neutrons for 
beta-radiation to take place, so that a nucleus will absorb neutrons 
until it can no longer hold them without changing its charge. 
Nuclei of higher and higher mass numbers are produced as the 
nuclei become richer and richer in neutrons. The final result of the 
capture of fast neutrons is the formation of the natural radioactive 












Number of 


Atomic 


Element 


Mass 


neutrons 


number 




number 


14 


12 


Magnesium 


26 




13 


Aluminium 


27 




14 


Silicon 


28 


20 


18 


Argon 


38 




19 


Potassium 


39 




20 


Calcium 


40 


28 


22 


Titanium 


50 




23 


Vanadium 


51 




24 


Chromium 


52 




26 


Iron 


54 


50 


38 


Strontium 


88 




39 


Ytterbium 


89 




40 


Zirconium 


90 




42 


Molybdenum 


92 


82 


54 


Xenon 


136 




56 


Barium 


138 




57 


Lanthanum 


139 




58 


Cerium 


140 




59 


Praseodymium 


141 




60 


Neodymium 


142 




62 


Samarium 


144 


126 


82 


Lead 


208 




83 


Bismuth 


209 








| 1 | 1 


i ' i ' i 




260 


\ fission 






— 


240 


Cf 254\\ 






220 


~" \ \ 






— 


200 


alpha (S \ 
_ decay 1 ^v.l_ 






- 


180 


ft V" 


N=126 




__ 


160 


subsequent / W, \ 
beta decay ' S \ 


« 




- 


140 
120 
100 


| slow capture/ 
path (n. ? ) 

— 1 


i l 1 


>^.N=82 


- 


80 


S 


^\] 1 , rapid capture 
^A path (n.j,) 

\I>- N=50 


- 


60 




Fe 56 _il 


— 


40 






- 


20 




N e 22_i> 


— 




i,i, 


1,1,1 


\ 



109 



100 90 80 



70 60 50 40 

atomic number (2) 



30 20 10 



38 The formation of elements by the capture of slow or fast neutrons. The 
diagram shows the path followed in the plan (atomic weight, atomic number) 
according to whether the capture is slow (so that the radioactive nuclei have 
enough time to decay before capturing another neutron) or fast (so that the 
nuclei capture neutrons one after the other until the whole nucleus becomes 
unstable, so that electrons and neutrinos must be emitted before the capture of 
neutrons can continue). The first process leads to the formation of elements 
such as the rare earths ; the second, especially associated with supernovae, io 
the formation of radioactive elements. 



elements. Indeed, the formation of radioactive elements cannot be 
explained without bringing in the capture of fast neutrons, because 
capture must lake place so quickly that the radioactive elements 
arc formed before they have lime to decay! 

It can be shown that the formation of rhenium- 1 87 is certainly 
due to the capture of fast neutrons, while osmium- 1 86 and osmium- 
187 are equally certainly due to the capture of slow neutrons. All 
this is of great importance in drawing up our cosmical chronology, 
as described on page 91. The initial abundance of osmium is 
particularly significant. 

The fast processes occur in supernova?, and an enormous flux of 
neutrons can then irradiate elements of the iron family. This, also, 
is highly significant. It is also worth noting that the formation of 
highly unstable elements, which soon break up by fission into 
several large parts, explains why some elements appear to be rather 
surprisingly plentiful in comparison with other members of the 
same elernenl-family. 

The various nuclear processes described above may be con- 
veniently summarised in table 8, though it must be remembered 
that not all these processes necessarily take place in the same stars. 

The chemical composition of matter in the Galaxy 

Earlier in this book, something was said about the way in which 
spectral analysis leads to the knowledge of what elements are 



39 Details lo show how elements are formed. The thick line marks the slow- 
capture process ; the dotted arrows indicate the beta -process and associated 
phenomena. Osmium-1 86 and osmium- 1 87 cannot be produced by the fast- 
capture process because the series stops at tungsten- 1 86 and rhenium- 137, 
which have a very long half- life. Osmium-186andosmium-187, therefore, 
must be due to the slow capture process. 



Ill 















0S184 






0s186 


0s187 


0s188 


0s189 








p 


















Re185 

r 


J 

89hr 


Re 187 


k 


* 


CO 










W182 

r 


W183 


W184 


X 

76d 


W186 


n 












Ta181 


J 








| 


* 








I 




















! 

■ 
i 
■ 
i 
















s- process 



























present in the outer layers of a star. Iron may be taken as a good 
example. It is obvious that the dark absorption lines due to iron 
in the star's spectrum will be strong or weak in proportion to the 
quantity of iron in the outer layers of the star. 

To work out a value for the colour index as defined by the ratio 
of yellow light to blue light, or of blue to ultra-violet, it is necessary 
to measure the amount of light sent out by the star over a con- 
siderable range of wavelengths. In measurements of this sort, no 
distinction is made between the continuous background and the 
spectral lines. However, it is clear that colour index values derived 
in this way depend upon the intensities of the absorption lines 
present in the spectrum. An exact relationship has been established 
between the quantities of metals (principally iron, titanium and 
vanadium) present in the outer layers of a star, and the value of the 
colour index. Colour indexes are much easier lo measure than 



Table 8 Reaction temperatures and periods of reaction for 
the principal nuclear processes 



Process 

Fusion of hydrogen 

Fusion of helium 



Temperature (°C) Duration 



20.000.000 



100.000.000 



10.000 million 
years 



Stars 

Main 
Sequence 



1 0.000.000 years Giants 



Capture of slow neuirons 300,000.000 10,000 years Giants 

Equilibrium process 3,000.000.000 10monihs Supernovae 

Capture of fast neutrons 10.000,000.000 10 seconds Supernovas 






details of spectra, and have led to much important information 
about the chemical compositions of the stars. All this is highly 
significant, loo, in studies of the globular clusters and the old 
stars in our Galaxy. 

Globular clusters 

Globular clusters are very beautiful objects, symmetrical in shape, 
and each containing tens of thousands of stars. All lie al a great 
distance from us. Altogether, 118 globular clusters are known, and 
colour index measures have been obtained for a dozen of them. 

The colour index diagrams for globular clusters always show 
one branch, characteristic of giant stars, extending from the Main 
Sequence. The ages of the globular clusters can then be estimated, 
by the same technique as is used for galactic clusters. The reliability 



112 






of the results depends partly upon the basic theory and partly upon 
the interpretation of the observational data, and there is bound to 
be a good deal of uncertainty, but it is at least safe to say that all 
the globular clusters are very old. The ages of Messier 13, Messier 5 
and Messier 3 have been given as 22. 24 and 26 thousand million 
years respectively, though doubts about the theoretical model 
mean that these ages may have been overestimated by a factor of 2. 
Colour index measures for stars in globular clusters indicate that 
there is a marked paucity of metals. Apparently the stars in M5 
and MI3 contain twenty limes less iron than the Sun. white the 
stars in M2 and M92 contain two hundred times less iron than is 
found in the Sun. It follows that globular clusters must have been 
formed from interstellar material which was relatively metal-poor. 

Old stars 

On page 50 it was noted that a star which has a high velocity in 
the direction perpendicular to the plane of the Galaxy can go well 
above or below the galactic plane, whereas slow-moving stars 
cannot travel very far from the plane. When the velocities per- 
pendicular to the galactic plane are correlated with colour indexes 
and metal abundances, a remarkable fact emerges. Stars which are 
richest in metals are also slow stars, moving at less than 50 kilo- 
metres per second, while metal-poor stars have velocities which may 
reach as much as 300 kilometres per second. 

In consideration of the relationship between velocity and 
maximum distance from the galactic plane, it seems that metal-poor 
stars must have been formed at any possible distance from the 
plane of the Galaxy out as Tar as 20.000 light-years, while metal- 
rich stars were formed much closer to the plane of the Galaxy, 
over a region not exceeding 1,000 light-years in thickness. 

The progressive enrichment of the Galaxy in metals, mainly 
because of the nuclear reactions inside the stars and the ejection 
of stellar material into space, makes it seem that metal-poor stars 
are old. whereas stars which are rich in metals are comparatively 



40 The g lobu lar c I uster O m ega Centa uri . 
The cluster appears circular although it is 
Co all intents and purposes spherical. 



113 




41 Ultra-violet excess and velocity 
in space. The velocities of the stars 
in a direction perpendicular to the 
main plane of the Galaxy are associated 
with metal abundance in their atmospheres. 
The ultra-violet excess is a measure of this. 



250 



r~r 



200 



150 



W 



100 



50 — 



306 382 



t t 



T~^ 



8 



o o 

OCD 
O O 

oo 



oo 



O o 



'°oo o " 



o_o 



8° 



• * 8 Q ° 8 



JO 



! 



00 8, 



OQO 



it Willis o.*s o8o a <*> ° 



2 max 

9000 
psc 

8000 



_ 7000 



_ 6000 



— 5000 



_ 4000 



— 3000 



2000 



1000 

800 

600 

400 

200 
100 



IIS 



00 



0-10 SlU-B) 020 



030 



young. Old stars were formed al a period when the main interstellar 
material was spread out to great distances on either side of the 
galactic plane, while the younger stars were produced when, as at 
present, most of the material was confined to a region relatively 
close to the plane. During the time when old stars were being form- 
ed, the Galaxy must have contracted toward its equatorial plane. 

Stars with large positive colour indexes move in very eccentric 
orbits. Paths of this sort can occur only when the star's velocity in 
the direction of the galactic centre is comparable with its velocity 
relative to the perpendicular to the plane of the Galaxy. The 
material from which old stars were formed must thus have had a 
considerable velocity in the direction of the galactic centre, and 
contraction toward the plane should be accompanied by contrac- 
tion toward the centre. If the rate of contraction were roughly the 
same as the orbital velocity, it can be shown that the contraction 
would have taken from 1 00 to 200 million years. Globular clusters 
must have been formed very quickly at the start of this phase of 
evolution of the Galaxy, and were left behind, at a great distance 
from the galactic centre, as the gas contracted. 

The sizes of the eccentric orbits of old stars show that the original 
cloud must have been about 300,000 light-years in thickness, since 
when it has contracted to one-tenth of this size in the equatorial 
plane and one-twenty-fifth in the perpendicular direction. The 
great contraction toward the galactic plane can be explained only 
by the effects of the general rotation of the whole system. 

Conclusion 

The ideas of time and chronology are fundamental in any under- 
standing of the universe. At the start of the present chapter, it 
was pointed out that astronomical events develop over periods of 
time, and that each kind of phenomenon has its own particular 
time-scale. Motion, energy transformation, radiation and radio- 
activity are entirely independent of each other, and each one may be 
used to define what we call "time". Moreover, it is a fundamental 



116 



postulate that 'time* as defined with reference to any one of these 
phenomena is always the same time, so that the chronology of a 
phenomenon C is the same whether it has been worked out 
according lo the lime-scale based on phenomena A or B. It is 
true that some physicists have cast doubts upon the coincidence of 
the different lime-scales, and this will be discussed in more detail 
later, but it must be said thai al the moment there is no valid 
method of deciding who is right and who is wrong. 

For ihe moment, at least, ii will be best for us to keep to the 
common lime-scale in summarising the points that have been made 
here. There can be no doubt that evolution is in progress all around 
us. The Galaxy has not always been in the state that it is in today; 
the stars in the Galaxy are born, change, and so far as most are 
concerned, probably end by disappearing from our view to wander, 
dark and invisible, through the Galaxy. 

Studies of star-clusters lead on to estimates for the ages of some 
systems. The oldest of these systems have an age of perhaps 15,000 
million years, while the youngest date back for less than one million 
years. Observation even indicates that star-formation is taking 
place before our eyes; the most striking example is that of the star 
FU Ononis, which became luminous in 1937 over a period of less 
than three months in a position where there had previously been no 
definite star and where there had been nothing more than some very 
dim object. The researches now going on will presumably lead on 
to a better knowledge of the very earliest stages ofa star's evolution. 

Various remarkable events can happen during stellar evolution. 
In some cases, marked chemical transformations due to nuclear 
reactions modify the composition of the stars concerned, and a 
large fraction of the material is hurled out into interstellar space, 
thereby causing a slow but steady change in the chemical composi- 
tion of the interstellar material; metals become more and more 
abundant. It is likely that activity of this kind was more intense 
in the early history of the Galaxy than it is now. A few stars seem 
to suffer violent outbursts which end as supernova explosions; it 
is probable that during this process, radioactive elements are 



117 



regenerated. Of course, nothing certain is known about the time 
when the regeneration process and the formation of the radioactive 
elements began, but it may have been something like 18,000 million 
years ago. 

The rapid evolution of the Galaxy soon after its formation 
affected both the chemical composition and the form. Flattening 
soon took place, so that old, metal-poor stars are situated well 
away from the galactic plane, while young, metal-rich stars are 
found much closer to the plane. And without being too hard and 
fast about it. there is reason lo ihink that the distinction between 
Populations 1 and II are associated with age and composition. Stars 
of Population I are young and metal-rich, while stars of Population 
II are old and metal-poor. 

At ihe present time, all these problems are being closely studied 
by astronomers; more is being learned about stellar structure and 
evolution, and about the chemical composition of stars and nebulae. 
Just as the study of the Sun is of fundamental importance in 
finding out more about other stars, so the study of our Galaxy is 
vital in any attempt to understand other galaxies. Yet the almost 
incredible varieties or forms presented by the outer systems lends 
support to the view that some of the mysteries of our Galaxy will 
be solved when we have been able to interpret the other galaxies 
lying far away across space. 



4 Space and the galaxies 



Photography shows that there are enormous numbers of galaxies, 
diffuse objects of regular outline. The brightest of them are also the 
closest to us, and can be resolved into stars. The more remote 
galaxies cannot be so resolved, even with our most powerful 
instruments, so that they look like dim, nebulous patches. 

Even a cursory study of the photographs shows that the galaxies 
may be divided into two main classes. Some galaxies, rich in blue 
stars and interstellar gas, arc of spiral structure; they arc flattened 
and give clear indications of quick rotation. Others, poor in blue 
stars, have no spiral structure and are much less flattened, but they 
give the impression of an ellipsoid in a state of rotation, and are called 
elliptical galaxies. Actually, the classification of galaxies is much 
more complex than might be thought at first sight, and this is one 
of the problems to be examined in the present chapter. First, it 
will be helpful to list a few of the questions to be tackled. 

The positions in space of the galaxies must be determined. This, 
of course, brings us back to the old problem of distance-measuring, 
but geometrical and kinetic methods, so useful in estimating the 
distances of stars in our own Galaxy, are of no use for the external 
systems; the distances involved are much too great, and the proper 
motions of galaxies are too slight to be measured at all. Less direct 
methods have to be found, based chiefly upon the intrinsic 
luminosities of the galaxies concerned. 

The next problem is that of classification of the different types 
of galaxies, bearing in mind their stars, their gas. and their shapes. 
With stars, our physical knowledge is good enough to provide a 
sound basis for classification, but this is not true for the galaxies. 
So little is known at present that there is no choice but to follow 
methods of analysis resembling the methods once used by natur- 
alists in classifying plants and animals. 

A third problem, serving as a kind of introduction to an overall 
study of the universe, involves finding out the distribution of the 
galaxies in space. This does not mean the general distribution all 
through the universe, but refers to the grouping of galaxies in 
systems. Moreover, the masses of the galaxies must be investigated. 



119 



I 
I 



42 A diagram showing the types of 
galaxies. This system of normal 
spirals, barred spirals and elliptical 
galaxies was devised by Hubble. Wuh 
some modification it is still used, 
although there are serious doubts 
whether ii represents any kind of 
evo lutionarysequence. 




120 43 The 120-in reflector ai the Lick 

Observatory, USA This has a skeleton tube 
and a conventional mounting. It is one of 
the most recent of the great reflectors 
and is second in size only 
to the 200- in reflector at Palomar. 



since this leads on lo a knowledge of ihe mean density of matter in 
space. 

The development of the special science known as cosmology, to 
be discussed in the last section of the present book, depends largely 
upon a sound knowledge of the galaxies. Summing up. it may be 
said that we need information about: (a) the distances of the 
galaxies, (b) luminosities, (c) classification of different types of 
galaxies with respect to form and content, (d) distribution of the 
galaxies in space, and (e) the masses of the galaxies. 

The distances of the neighbouring galaxies 

There are several ways in which the distances of relatively nearby 
galaxies can be measured. In each case, certain bodies in the 
galaxy concerned are studied, and their intrinsic luminosity 
measured. As soon as the real luminosity is known, together with 
the apparent brightness, the distance of the object can be worked 
out. and this, of course, also gives the distance or the galaxy in 
which the object lies. 

Effectively, the relationship between apparent magnitude and 
absolute magnitude is a clue to the distance of the object. When 
the magnitude differences are. respectively: 0. 1.2, 3, 4, 5. 6, etc. 
the distances involved are, in parsecs, 10, 16. 25, 40, 63. 100, 160, 
and so on. (One parsec is equal to 3-26 light-years.) For example, a 
difference of 35 magnitudes corresponds to a distance of 100,000.000 
p. usees, or about 326.000.000 light-years. 

Something has already been said about the period-luminosity 
law of Ccpheid and RR Lyrae variables, according to which the 
distances of these variables can be found as soon as their periods 
of fluctuation are known. Clearly, the method can be applied to 
the galaxies. When a suitable variable has been discovered inside 
a galaxy, and its period measured, its distance can be found; and 
this leads on to the distance of the galaxy which contains the 
variable. 

Nova? are also very useful. They are important in many ways, and 




122 



represent stellar outbursts on a grand scale, (hough they are much 
less violent than supernovas, and after its outbreak a normal nova 
returns to something like its former condition. Many novs have 
been observed in our Galaxy, and they occur in other systems also. 
Though the absolute magnitude of any individual nova may not 
be known, statistical methods show thai in our Galaxy, the mean 
absolute magnitude of a nova at maximum is —7-5. If a nova is 
seen in an external system - the Andromeda Galaxy, for instance, 
where many novse have been discovered it is reasonable to 
assume that the maximum absolute magnitude is also —7-5. 
Comparison of this value with the observed apparent magnitude 
then gives the distance. 

Over a hundred globular clusters are known to be associated 
with our Galaxy; each is symmetrical, and each contains a large 
number of stars. Their distances have been measured (by means of 
their RR Lyra stars), and their absolute magnitudes have been 
calculated; the value adopted is —7-5. Globular clusters are also 
known to be associated with other galaxies; and if these too have 
absolute magnitudes of about —7-5. their distances can be worked 
out in the same way as for novae. 

Another method can be used for galaxies which are close enough 
to be resolved into stars. The brightest of the red stars in galactic 
globular clusters are compared with the brightest of the red 
stars in the galaxies, and it is assumed, very reasonably, that the 
absolute magnitudes are the same. Comparison of the absolute 
magnitudes with the apparent magnitudes then leads to values for 
the distances involved. 

These various methods are applicable only to the relatively few 
galaxies close enough to be resolved into stars. The results are as 
follows: 

1 Small Magellanic Cloud. Both the Large and Small Magellanic 
Clouds, which arc situated in the southern part of the sky some 
distance from the Milky Way, are satellite systems of our Galaxy. 
It is required to find out the distance modulus, which may be 



44 The dome of the 1 02- in reflector at the Crimean 

Asirophysical Observatory in the USSR. This 

photograph was taken in 1 960. when the dome was 

nearly complete. It is the largest telescope 

in the Soviet Union and is surpassed in size only 

by the Palomar 200-in and the Lick 1 20 -in reflectors. 



123 




defined as m - M, in which m is the apparent magnitude and M 
the absolute magnitude. For the Small Cloud, the distance modulus, 
as obtained by various methods of investigation, is as follows: 

m - M 



METHOD 


DISTANCE 


MODULUS 


Short-period variables 




191 


Novae 




18-7 


Novas 15 days after maximum 




188 


Red giants in globular clusters 




19-1 



The mean value is 18-9. When the effects of absorption arc allowed 
for, adding about 0-5 to the apparent magnitudes of stars in the 
Small Cloud, the distance is found to be 55,000 parsecs. 

2 Large Magellanic Cloud. The distance modulus for the Large 
Cloud is measured in the same way. with the following results: 






124 



METHOD 

Short-period variables 

Red giants in globular clusters 

Classical Cepheids 

Nova: 

Nova; 15 days after maximum 



DISTANCE MODULUS, m - M 

19-2 

19 

18-6 

19 

18-4 



There is some disagreement here, and the correct result may be 
anything between 18-7 and 19, corresponding to an error of 
roughly 30 per cent in the distance estimate. If the absorption is 
held to add 0-4 to the apparent magnitude, the distance of the 
Large Cloud is found to be 45,000 parsecs, so that it is appreciably 
closer than its smaller neighbour. 

3 The Andromeda Spiral, Messier 31, Many methods have been 
used to measure the distance of this beautiful northern galaxy, 
whose apparent magnitude is 4-33. The results as obtained in 
different ways are: 



METHOD 

Photographic measures of the over- 
all magnitudes of globular clusters 
Photoelectric measures of the over- 
all magnitudes of globular clusters 
Brightest stars of Population II (red 
giants) 

Classical Cepheids 
Novs 



DISTANCE MODULUS, m M 



24-8 



23-9 

24-3 
23-9 

24-6 



The mean value is 24-4. Absorption increases the apparent 
magnitude by about 06, and so the distance was found to be 
about 550,000 parsecs or 1,800.000 light-years, with an absolute 
magnitude of about —20. Very recent studies have increased this 
slightly, and the latest value for the distance of the Andromeda 
Spiral is 2,200,000 light-years. 



45 An unstable system 
of multiple galaxies: 
Stephen's Quintet. 







126 



Table 9 The most luminous stars in various gal 


axies 


Star 


Galaxy 


Absolute 


Distance 






magnitude 


modulus 


N 12 VI Cygni 


Our Galaxy 


-98 


- 


Star in Scotpio 


Our Galaxy 


-9-4 


— 


Star in Orion 


Our Galaxy 


-8-8 


— 


HDE 26970 


Large Magellanic Cloud 


-9'8 


192 


ROC 269781 


Large Magellanic Cloud 


-9-5 


19-2 


HD 33579 


Large Magellanic Cloud 


-101 


19 2 


HD7583 


Small Magellanic Cloud 


-88 


19'2 


HD6884 


Small Magellanic Cloud 


-8-5 


19 2 


Mean value 


Andromeda Spiral. M31 


-8-9 


24-6 


Mean value 


Triangulum Spiral. M33 


-8^6 


24-5 



Highly luminous stars 

To take matters a stage further, new distance-markers are required, 
and they are found in the highly-luminous blue stars contained in 
almost all galaxies (excluding certain dwarf systems consisting 
entirely of Population II). The absolute magnitudes of these highly- 
luminous stars may be worked out. whenever the distances of the 
galaxies in which they lie have been measured in other ways. The 
results are given in table 9. 

If similar stars of high luminosity are found in remote galaxies. 
they can be used as standards of reference for distance-finding. 
They can be seen out to greater distances than the short-period 
variables, because they are much more luminous. Taking the 
absolute magnitudes for the brightest blue stars in galaxies as 
—8-5, the following distance moduli are obtained: 



127 



GALAXY 
M81 

M87 
MIOO 

NGC4321 



DfSIANCH MODULUS, m - M 

27 
308 
293 
30' 8 



One difficulty about this method is that the exceptionally luminous 
stars may be surrounded by bright gaseous nebulosity, not easy to 
recognise. If the nebulosity is unwittingly lumped together with the 
star, the resulting magnitude error can be as much as 1-8. The only 
remedy is to compare photographs taken in blue and in red light, 
so that the blue supergiants can be distinguished from any bright 
nebulosity nearby, and the required corrections can be made. 
The values of the distance moduli for M87 and NGC 4321 involve 
adjustments of this kind. 

Clusters of galaxies 

Sky photography shows that galaxies often group together in 
systems which are called clusters of galaxies. Various clusters have 
been found, of which those in Virgo, Ursa Major, Coma and 
Bootes are particularly notable. Some are comparatively close; 
others, such as the cluster in Hydra, are extremely remote by any 
standards. 

The number of galaxies detectable in a cluster depends upon the 
limiting magnitude of the instrument used. For instance, the rich 
cluster of galaxies in the constellation of Coma is shown to have 
654 members on a plate taken with the 18-inch Schmidt telescope 
at Palomar. but as many as 10.724 members on a plate taken with 
the 48-inch Schmidt. The first instrument showed galaxies in the 
magnitude range from 13-2 to 16-5, but the 48-inch could reach 
down as far as magnitude 19-0. 

The clusters include galaxies of all types: elliptical, spiral, and 
in great numbers, flattened systems without spiral structure, and 
devoid of interstellar material. These latter systems are classed as 
galaxies of type SO, In addition, the clusters contain objects of 



128 



46 NGC 205 photographed with the 200- in Hale reflector at Palomar. 

This is an elliptical galaxy and is a companion or 'satellite galaxy' 

to the Andromeda Spiral, M31 . It is probably true to say that 

N G C 2 5 a nd t h e seco nd sa t e 1 1 u e ga I a xy b ea r t he sa me r el a 1 1 a nsh i p 

to M31 as with the two Magellanic Clouds in the case of 

our own Galaxy, though the types are not the same. 



129 






different brightness, so thai attempls can be made lo draw up a 
statistical analysis of the magnitudes or individual galaxies in a 
cluster. The number of galaxies with magnitudes between m and 
m + I, m + 1 and m+ 2. m +2 and m + 3, and so on, is counted, 
and what is termed a luminosity function is obtained. The similarity 
of the luminosity function for different clusters is quite remarkable. 
Another method is to arrange the separate galaxies in order of 
decreasing brilliancy, and then consider, for instance, the brightest 
ten, comparing them with the ten brightest members of a separate 
cluster. Here, too, there seems lo be surprising uniformity between 
the clusters. In twelve cases, for instance, the difference between 
the magnitude of the brightest separate galaxy and the tenth in 
order lies between 0-74 and 1 -73. with a mean value of 1 '29. 

All these results seem to show that the clusters of galaxies are 
of Ihe same basic kind, and have the same basic origin. In the 
following discussions, it will be assumed that the mean absolute 
magnitude for the ten brightest galaxies in a cluster is always Ihe 
same. This may not be strictly true, but it is not likely to be very 
wide of the mark. Of course, as soon as the absolute magnitudes 
of the brightest galaxies in a cluster have been found, the distance of 
the cluster itself can be worked out. So far, this process has been 
carried out for 18 clusters. 

The absolute magnitude of the Andromeda Spiral is —20-3, 
while for NGC 4321 and M87 in the Virgo cluster the values arc 
respectively —20-91 and — 20'96. The mean absolute magnitude for 
the brightest galaxy in a cluster can be taken to be —21. With this 
value, the distance modulus for the Hydra cluster is 40. Neglecting 
any corrections, of which more will be said later, this corresponds 
to an approximate distance of 1,000 million parsecs, or 3.CMX) 
million light-years. 

The red shift , 

The first observations of the spectra of galaxies were made by 
.Slipher in 1912. On his photographic plates, Sliphcr was able to 





131 



measure the radial velocities of the galaxies, by means of the 
Doppler effect, and by 1925 he had obtained results for 49 galaxies. 
Most of the Doppler shifts were toward the red end of the spectrum, 
indicating velocities of recession. Using these results, E.E.Hubble, 
in 1929, was able to establish a definite relationship between 
distance and the velocity of recession. Two years later, Hubble and 
his colleague M.Humason obtained important results from 
studies of the clusters of galaxies, and drew up the so-called 
Hubble-Humason law linking distance with radial velocity. The 
value which they obtained was 550 kilometres per second per 
million parsecs. 

A good many corrections have had to be made to this value, 
mainly because of errors in the absolute magnitudes of the objects 
used in the compilation of the Law. The constant H of Hubble 
and Hu mason's relationship is fixed nowadays in three stages: 






1 The mean apparent magnitude of the ten brightest galaxies in 
a cluster is determined, and the amount of the red shift in the 
spectral lines is measured. Using the value for the red shift as 
measured, it is possible to determine the section of the spectrum 
which is seen and to calculate the apparent magnitude that the 
galaxy would have in the absence of any red shift. To some extent. 
of course, the correction depends upon the spectral characteristics 
of the galaxy, but this can be allowed for. For a red shift correspond- 
ing to a recession of 60,000 kilometres per second, the correction 
has a value of 0-94. 

2 Taking the red shift, expressed as a fraction of the velocity of 
light, as a function of the mean apparent magnitude which has 
already been found (corrected for the effects of the red shift and 
also for the absorption experienced by the light when crossing our 
Galaxy), a relation can be found between the corrected apparent 
magnitude and the red shift. This leads to an exact relationship 
between red shift and distance. 

3 The scale is then fixed by means of the absolute magnitude of the 
ten brightest galaxies in a cluster. 

Take, for example, the cluster in Hydra. The radial velocity is 
0-2 of the velocity of light. The next steps are to apply corrections 
of 0-94 because of the red shift, and 0-49 on account of absorp- 
tion in our Galaxy. With an absolute magnitude of —21. the 
derived distance modulus is 38-77, corresponding to a distance of 
520,000.000 parsecs or 1.700.000,000 light-years. 

What emerges from these investigations is a linear relationship 
according to which the radial velocity of recession increases by 
100 kilometres per second per million parsecs. On this reckoning, 
the distance of the Hydra cluster would work out at 600,000,000 
parsecs or 1,950.000.000 light-years. The value for the Hubble- 
Humason Law adopted at the moment {100 kilometres per second 
per million parsecs) is naturally not definitive, and will no doubt be 



1 32 48 The distribution of clusters of galaxies 

overs certain region of sky (after Zwicky}. 
Each figure corresponds to a radial velocity interval : 
(a) below 1 5.000 km/sec ; (b) 1 5,000 to 30,000 km/sac ; 
(c) 30,000 to 45.000 km/sec ; (d) 45,000 to 
60,000 km/sec ; (e) over 60,000 km/sec. 



improved in the future, but it serves very well in estimating Ihc 
distances of very remote galaxies, and it has to be used when we 
are trying to reach out to the furthest limits accessible to us. 

Classification of galaxies 

The preliminary classification of galaxies given at the start of this 
chapter is. of course, inadequate. Several methods of more detailed 
classification are possible. The first of these, used extensively by 
Hubble, depends upon the morphological aspects of the galaxies 
as observed optically. Another is based upon spectroscopic studies. 
Particularly in the characteristics of the radio emission. 

Optical appearance 

As has been noted, galaxies may be classified as either elliptical 
or spiral, but more properly there are four main classes to be 
considered: elliptical (type E). lenticular (SO), spiral (S) and 
irregular (I). This is Hubblc's classification. 

The so-called elliptical galaxies range from globular forms lo 
very elongated lenticular shapes. In general, they show no structural 
details other than the small, bright nucleus, around which the glow 
of the galaxy fades away in each direction until it is lost against the 
dim luminosity of the night sky. 

Lenticular galaxies are characterised by a bright nucleus lying 
a I the centre of the lenticular disc, which has a fairly sharp 
boundary surrounded by a feeble, diffuse envelope. In their 
generally flattened forms they bear some resemblance to the spirals, 
but they contain very little interstellar material, and there is of 
course no spiral structure. 

In the spiral galaxies, there are various spiral arms which may be 
open or tightly-wound. Hubble distinguished two families: the 
normal spirals, with arms coming out tangenlially from the central 
bright nucleus, and the barred spirals, in which the arms come from 
the ends of a bar crossing the bright nucleus. The amount of 



+16 . • .. ...» 



(a) 



+ie:. 



-4° 



lb) 



16" 



i 
12" 



i 
8 h 



" • ••.' '. . " f- * • *■ " *v* ..-■.■•■- • 

• ■ * •'-i '.■•*.;'.. ■■ ■ . ■ . • 

*• • ..*••- if •.-'•••. • * •••• • * » • ■. w 



4 - 4* *' 



16 h 



i 
12* 



i 

8" 



+16° 



-4° 



ic) 






16" 



12" 



8- 



+16°. « 

-4° 






« • 



i 

16" 






12" 



*■ -v :/,*■• * 



i 

8- 



+16° 



-4° 



•tv 



>■'. 



w *■ • * »/ 
■ V m . ■» V ft. 






16" 



12 h 



134 



opening of the arms is shown by the letters a, b or c; thus Sa 
spirals are tightly-wound, while with Sc systems the spiral is very 
loose. 

Irregular galaxies, as their name implies, are structureless. Into 
this class Hubble put all the galaxies which did not seem to fit 
into any of the other types. 

Strictly speaking, the classification of galaxies cannot be limited 
by a simple division into four large classes. There are inter- 
mediate types, and it is even possible that there is a continuous 
gradation from the ellipticals right through to the irregulars. 
However, a classification of such a kind would be intelligible only 
if we could solve the problems of the forms of the galaxies, and it 
must be admitted thai no such theory is available as yet, although 
some basic ideas have been proposed. 

Spectral classification of galaxies 

No classification can be based upon spectral results only; it must 
also be morphological. The following are the main types: 

1 Spirals'. These are classified by means of a comparison between 
the brightness of the central region, and the total brightness of the 
galaxy. The centre of a galaxy will show a spectrum which is a 
combination of the spectra of all the various stars in the region, 
and it is bound to be somewhat confused, but it does give informa- 
tion about the main components of the area under inspection. 

At this point it is worth recalling that before colour index 
measures became so widely used, the stars were always classified 
according to the dark absorption lines in their spectra (a system 
which, of course, is still in use). The main types were: 

B: bluish-white stars, with prominent helium lines in the soectra. 

A: white stars, with prominent hydrogen lines. 

F: yellow stars, with prominent spark-lines of metals. 

G: yellow stars, with arc-lines of metals. 



135 



K and M: orange-red stars, with spectral lines due to the molecules 
of metallic oxides. 

By analogy, the composite spectra of the centres of galaxies are 
indicated by the letters a, f. g and k. The use of these letters is 
enough to distinguish between the spirals, because the relative 
brightness of the centre to the overall brilliancy is closely related 
to the spectral type. There is. therefore, an approximate relation- 
ship between Hubble's types Sa, Sb and Sc, classified by the 
increasing opening of the spiral arms, and the spectral types of the 
centres, as follows: 

Sa kS 

Sb g S - gk S 

Sc a S - rg S 

with types gk and fg being intermediate between g and k, and f 
and g. respectively. 

2 Ellipticals. The classification is essentially the same as Hubble's. 

3 D-galaxies. These galaxies are distinguished by an elliptical 
nucleus surrounded by an extended envelope. Some of them would 
have been classed as SO in Hubble's system so far as their optical 
aspect is concerned, but the correspondence between the two 
classifications ends there, because all the SO galaxies arc very 
flattened, while no flattened D-type galaxy has ever been observed. 
There is a large range of luminosity, with the brightest galaxies 
being at least ten times more luminous than the feeblest. What may 
be called supergiant D-galaxies, found near the centres of some 
clusters, have diameters three or four times greater than those of 
lenticular galaxies of the same cluster. 

4 'Dwnb-beir galaxies. These are analogous to the D-galaxies, but 
each has two nuclei in the same envelope. This may be an extreme 



136 



case of multiple, tightly-packed galaxies in which there are only two 

equal components. 

5 N-galaxie.\: A galaxy of this class has a bright uncleus, stellar in 

appearance, which is responsible Tor nearly all the light coming 
from the system. It is surrounded by a faint nebulous envelope, 
which does not stretch outward for very far, 

6 Quasi-stellar sources (Qs). These remarkable objects, also known 
as quasars, will be described in detail later. Whether they can be 
classed with other galaxies remains to be seen. They are stellar in 
aspect, but sometimes accompanied by faint nebulous wisps. 
They emit intense ultra-violet radiation, and the emission lines in 
their spectra are broad. 



Radio sources 

In 1946 Hey, Parsons and Phillips were studying the continuous 
radio emission from the Milky Way when they discovered some 
small discrete sources, which did not agree in position with bright 
stars. More than 2,000 of these discrete radio sources have now 
been catalogued. To identify them with optical objects is as difficult 
as it is important; the optical objects are usually faint and, to make 
matters worse, the position of a radio source can seldom be fixed 
as accurately as with an object which can be observed visually - 
simply because a radio telescope is very much inferior in resolving 
power. At the present moment, a large number of radio sources 
have been conclusively identified with optical objects, many of 
which are galaxies. No doubt the list of identifications will grow 
quickly in the future. 

The power of a radio source may be measured either by con- 
sidering the total amount of energy sent out in the radio range, or 
else by means of a 'radio magnitude' based on the intensity at a 
wavelength of 190 centimetres. If both optical magnitude and radio 
magnitude are compared, it becomes clear that galaxies may be 



137 



divided into two classes: weak radio sources and intense radio 
sources. This division is confirmed by examination of the total 
radiative power. If the strength of emission in the radio range is 
plotted, and different symbols are used for the different types of 
galaxies, a sharp separation is found between strong and weak 
sources at about 10" ergs per second. However, the separation 
between strong and feeble radio sources undoubtedly takes place 
at a power lower than this. 

Radio sources can also be classified by means of a spectral index, 
which shows the manner in which the amount of emitted radiation 
varies as a function of the wavelength. In this way, sources in which 
the radiation is of thermal origin can be distinguished from those in 
which the emission is of the synchrotron type. 



Optical appearances of radio sources 

All the spiral galaxies belong to the group of weak radio sources. 
The strong radio sources are galaxies of type D dumb-bell, N and 
Qs, with radio sources of type D showing the greatest range of 
radio power (in the ratio of 10.000 to 1). 

The most powerful and luminous oT all these objects are the 
quasars, or quasi-stellar objects. In the radio range, their power 
ranges from 2-10-'-' to 2*10* 1S ergs/second, or from 50,000 million to 
500,000 million times the power sent out by the Sun. Table 10 
gives the radio power, absolute magnitude, distance and radio size 
for four quasi -stellar objects for which the speed of recession is 
known fairly satisfactorily. The main details have been calculated 
on the basis of Hubble's constant, taken as 100 kilo met res /sec per 
megaparsec. The high luminosity of these objects is particularly 
notable; it amounts to almost 100 times the brightness of the 
brightest normal galaxies. The power sent out in the optica! range 
by the quasi-stellar sources is truly enormous; 300,000 million 
times that of the Sun in the case of 3C-47, as much as 2.000,000 
million times that of the Sun for 3C-273. To make the situation 
even stranger, it is found that some of the objects, including 3C-47 



138 



Table 10 Data for quasi -stellar sources 

Name v {km/sec. ~') L (radio) Mv 



3C-47 
3C-48 
3C-147 
IC-273 



127,500 
110.100 
163,500 
47.400 



1 5x 10" 
4-7 x 10" 
2x 10" 
3x 10" 



-23 
-25 
-25 

-26 




1 39 



rnegsparsecs 
1,280 250 
1,100 3 
1.640 10 
470 40 



d (radio) 

kitoparsecs 

250 

3 

10 

1 



and 3C-273, are variable; their fluctuations can amount to 45 per 
cent of the total brilliancy over a period of time of only a month. 
This represents a variation in power of several hundred thousand 
million times the luminosity of the Sun, and at the moment we have 
to confess that we do not know what causes the fluctuations. In 
addition to a continuous spectrum, a quasi-stellar source shows 
in the optical range an emission spectrum of great intensity, and in 
comparison with the normal galaxies the spectrum of a quasar is 
distinguished by the fact that a great excess of ultra-violet radiation 
is emitted. 

Incidentally, it is worth noting that there are no very flattened 
galaxies among the strong radio sources, while weak sources, 
including most of the spirals, are strongly flattened. This alone 
suggests thai there are fundamental differences between the strong 
and the weak radio sources. 

Radio properties of different optical types 

A weak source always occurs as a single source centred upon a 
galaxy; its diameter may be smaller than, or comparable with, that 
of the galaxy concerned. The double structure characteristic of 
strong sources is never found with weak ones. It seems, therefore, 
that the central regions of spiral galaxies are responsible for the 
radio emission, and the cause may well be expansion and violent 
turbulence of the gas in the central region, as with our own Galaxy. 






In the radio range, the strong sources show a characteristic 
double structure, so that in most cases the radio waves come from 
two regions placed symmetrically to either side of the galaxy con- 
cerned (Lcqueux). Some of the strong single radio sources probably 
do not betray their double nature simply because our instruments 
are not sensitive enough to resolve them. However, not all the 
strong sources show the same optical properties. The weakest D 
and F. galaxies are single sources, and so are most of the dumb-bells. 
It is quite on the cards that most of the D, E and dumb-bell 
galaxies really are single sources, which would mean that double 
sources would be in an overall minority. The structure of N- 
galaxies in the radio range is decidedly complex, and the quasi- 
stellar objects (Qs) show all possible aspects - single, double, single 
but surrounded by a halo, and so on. It may be that these differences 
are due to nothing more than differences in the progress of evolu- 
tion, but it is impossible to be sure. 

The radio radiation of the strong sources is essentially due to the 
synchrotron process, caused by high-energy electrons. The problem 
of the energy supply of the intense radio sources is so important 
that it will be examined in more detail later. 



Multiple galaxies 

No classification would be complete without including the multiple 
galaxies. These are systems of two or more galaxies in association, 
and often connected by a bridge of faintly luminous material 
stretching across the space between them. 

To understand why the multiple galaxies are so significant, it 
will be helpful to return to elementary celestial mechanics, and say 
something about the properties of bodies in motion. The motion 
of two bodies can be either elliptical, hyperbolic or parabolic. 
Bodies which are moving in ellipses relative to each other will be 
permanent neighbours in space, while with parabolic or hyperbolic 
movement the association will be no more than temporary; once 
they begin to separate, the two bodies will continue to move apart 



[40 




3C 273 




Qs 3C 445 




3C310 




3C353 



141 




49 Various types of optical objects 
producing radio emission. All those 
illustrated in the diagram are extra- 
galactic. (After W.W. Morgan). 



3C 317 



cD4 






3C274 



E2 



38 



39 



40 



5 




X 


S 

0' 




1068 


B 






V 






i 












■ 






-5 


41 


■M 


o 






CJ 






Lfl 






•*; 






u 






F 







42 



43 



d4 



45 _ 



X Ml 01 



^X M31 

j^4490 
X 4258 

XX M82 



Vir A 



© 
© 



F °( A _ c^ 4782-3 

Cen A *-w©\0 °~° 7236_7 

Per A C ,-P "20 

c© °o 

O o-o 3C . 445 

*© °o 

© On 

Hya A^VJ 

O 



o — 



0°3C-227 

Pic A 

O 3C-234 



Q Her A -<£»- 3C-47 

QcygA 



^ 3C-273 
"V" 3C-48 



Q 3C-295 -^3C-147 



50 S c h e ma 1 1 c c I ass i f ica t io n of f a d i o 
galaxies according to radio flux and 
optical type. (After Mathews and Morgan). 



143 



O 
© 

o 

■$■ 

o — o 



Spirals and Irregulars 

Ellipticals (Class E) 

Bright Nuclei and extended envelopes (Class D) 

Intermediate between classes and E 

Brilliant, star-like nuclei and less extensive envelopes (Class N) 

Quasi -stellar sources 

Dumbbells (Related to D systems) 



indefinitely. With a triple system, things are much more compli- 
cated, and much work remains to be done on this notorious "three- 
body problem*. However, if two of the three bodies are close 
together and the third a long way away, the motion of the two 
nearby bodies will be very similar to that of iwo bodies, because 
the effects of the third may be more or less neglected. Also, the two 
nearby bodies may be regarded as 'one', and when considered with 
the remote third body we are again back to something like the 
much simpler two-body problem. In this manner, a triple system 
may be permanent, so that its members will always stay at a 
finite distance from each other. 

As a general rule, a third body approaching a two-body system 
will move in a hyperbola and will go off to infinity, after having 
perturbed the motions of the two bodies when at its closest to them. 
However, there is a slight possibility that the third body will 
approach in such a way that it will be captured by the two-body 
system. It is also possible that during the encounter, any one of the 
three bodies will be expelled from the system along a hyperbolic 
orbit. However, in most cases the final result will be that the three 
bodies will separate from each other, particularly when at ihe 
start of the encounter, the three bodies are roughly equidistant. 

All this applies equally to quadruple systems, whose stability 
depends essentially on the way in which the four components 






51 The radio source NGC 1275 in Perseus, photographed with the200-in Hale 
reflector at Palomar. Extragalactic radio sources were once thought to be due to 
galaxies in collision, but this idea has now been abandoned because the collision 
process would not provide nearly enough energy to account for the radio emission, 
Unfortunately it must be admitted that the reason for this great power in the 
radio range, shown by the Perseus source and others, is still unexplained. 



145 




146 



147 



are placed in space. A system in which ihc Tour components are 
roughly equidistant from each other makes up a 'trapezium', 
and in 1950 the Armenian astronomer V.Ambartsumian of the 
Soviet Union showed that such systems dissociate quickly, so that 
the components go their separate ways. 

Ambartsumian also drew attention to the properties of multiple 
galaxies. U is true that a double galaxy will follow much the same 
rules as a binary star, so that a two-galaxy system can last in- 
definitely, but the situation for a triple-galaxy system is different, 
and cannot be compared with that of a triple-star system. Some 
multiples are stable, but others are temporary, and are due only to 
the chance passing-by of independent galaxies. Many permanent 
systems are known, but only a few temporary ones have been 
observed as yet. Some temporary systems coincide with radio 
sources, and it used to be thought that strong radio sources might 
be due to galaxies in collision, but unfortunately this attractive 
theory has had to be given up, because the colliding process would 
not provide as much energy in the radio range as is actually 
observed. 

Many types of multiple systems have been found, and it often 
happens that several kinds of structures can be combined in the 
same galaxy. In our own Galaxy there is a vast halo of Population 
II stars together with the interstellar gas and Population I stars of 
the spiral arms, so that in a way it may be said that our Galaxy is 
a combination of an elliptical galaxy with a spiral. In one par- 
ticular system, it is possible that there may be normal spiral 
structures, barred spirals, and ellipticals. These different structures 
correspond to the coexistence, in the same system, of sub-systems 
in different states of motion. 

Galaxies may be very close to each other, and yet clearly separate. 
There are, for instance, some double galaxies which seem to be 
revolving round each other, much as with the components of a 
binary star. And in other cases, two or more galaxies may be 
joined by faintly luminous bridges. There may be such a bridge 
between our Galaxy and the Large Magellanic Cloud, and there is 






certainly one linking the Andromeda Spiral with its barred-spiral 
companion NGC 205. A tightly-packed multiple system made up 
of five galaxies joined by bridges of material is of special interest; 
it is known as Stephan's Quintet, and consists of two ellipticals, 
two barred spirals, and one galaxy of less definite form. Systems in 
which the relative separations are wider (of the order of three times 
the diameter of each galaxy) may be linked by immense filaments of 
unknown nature. 

When multiple systems are studied with regard to stability, it 
seems clear that some of the systems cannot have existed for more 
than 1,000 million years. This fact is difficult to explain, and it 
introduces the problem of the origin of the galaxies, because it 
suggests that galaxies are being formed in the universe at the 
present time. 

Masses of galaxies 

A galaxy is a system in rotation, with the centrifugal force and the 
gravitational force in equilibrium. The mass of a galaxy can there- 
fore be worked out by a straightforward application of the law of 
gravitation, provided that the speed of rotation is known. The 
general idea is as follows: 

Newton's law of universal attraction states that the force between 
two bodies is proportional to the product of their masses, and 
inversely proportional to the square of the distance between them. 
For the sake ofsimplicity, lei us assume that the Earth and the other 
planets move round the Sun in circular orbits. It is then easy to 
explain Kepler's third law, according to which the squares of the 
periods of revolution are proportional to the cubes of the orbital 
radii. 

To all intents and purposes, for a body which moves with uniform 
velocity along a circle of radius r, the centrifugal force will be 
proportional to the radius of the circle and inversely proportional 
to the square of the period. The force exerted by the central body on 
the moving body is inversely proportional to the square of the 



148 



radius of ihe circle. This gives the simple proportion: 

4k-i- 



centrifugal force = - 
Kepler's third law then follows: 



= force of attraction. 



r3 



Gin 



The quantity G is the constant of universal gravitation. It can be 
dispensed with if the period P is expressed in years, the orbital 
radius r in astronomical units (one astronomical unit being the 
radius of the Earth's orbit), and the mass m in solar units (the 
mass of the Sun being taken as 1). The velocity of the circular 
motion is given by: 

yi Gm 

r 

Here, too. G can be dispensed with if/n is taken in solar units, the 
velocity is measured in kilometres per second, and the distance is 
given in parsecs. However, this means that a numerical coefficient 
must be introduced, giving: 



V 2 (km/sec) = 0-0044 



(/n/O) 

r (parsecs) 



where /w/Ois the mass in solar units. This, then, is a reliable way in 
which lo determine mass, thus: 

(m Ol = r (parsecs) x V s (km/sec) x 230. 

When the attracting body cannot be reduced to a central mass of 
very small size compared with the orbital radius. Kepler's law no 
longer applies and must be replaced by a more complex law 
worked out from the always valid law of universal gravitation. 

Some idea of the mass of our own Galaxy may be found if the last 
formula is taken, with r (orbital radius) = 10.000 parsecs and the 
orbital velocity of the Sun taken as 250 kilometres per second. The 



Table 11 













Distance 




Name of 




m/10 






modulus. 


Method 


galaxy 


Type 


m 


m*/L* 


Distance 


m-M 


used 


Our Galaxy 


Sb 












M31 


Sb 


450 


1-7 




24 6 


Rotation 


M32 


E 


1-8 


13 5 






Virial 


M33 


Sc 


8 


3 






Rotation 


M81 


Sc 


170 


11 




27 8 


Rotation 


NGC55 


Magell- 
anic 


20 io 40 


3 to 6 




24-6 


Rotation 


NGC157 


Sc 


60 


1-9 


24 Mpc* 




Rotation 


NGC253 


af. Sb Sc 


240 


12 


H 




Rotation 


NGC300 


Sc 


21 


9 




26-6 


Rotation 


NGC 720 


Es5 


75 








Rotation 


NGC1068 


gS2p 


20 


2-7 


H 




Rotation 


NGC 1084 


Sc 


12 


1 


H 




Rotation 


NGC1097 


SBb 


5io13 




16Mpc 




Rotation 


NGC 1355 


S8c 


22 to 34 




20Mpe 




Rotation 


NGC 21 46 


Sa 


20 


3 


12 




Rotation 


NGC2903 


Sc 


3-7 


55 


6Mpc 




Rotation 


NGC 31 15 


E7 


70 








Rotation 


NGC 3379 


E 


110 


12 






Vrnal 


NGC 3504 


SBb 


9 


07 


H 




Rotation 


NGC 3556 


Sc 


8 to 12 


1-5 lo 2 


H 




Rotation 


NGC 4278 


E1 


38 


16 


H 




Rotation 


NGC 4486 


EO 


1400 


33 


T60Mpc 




Rotation 


NGC 4528 


Sb 


120 


13 


H 




Rotation 


NGC 4594 


Sb 


200 


3 




30-8 


Rotation 


NGC 4531 


Sd 


24 


6 


4 4 Mpc 




Rotation 


NGC 5005 


Sb 


105 


63 


14-4 Mpc 




Rotation 


NGC 5055 


Sb 


60 


3 10 4 


H 




Rotation 


NGC 51 28 


DE3 


200 


13 


5 




Radio 
source 


NGC 5248 


Sc 


3 


4 


H 




Rotation 


NGC 5383 


SBb 


40 




H 




Rotation 


NGC 7479 


SBb 


16 




H 




Rotation 


VV254 




130 








Rotation 



• Mpc — meg o parsecs : one mega pars ttc = one million parsecs. 
Further explanations of rhisiabta are grven later 



24 


1 1 


1 


1 


1 1 




2 








X / 


- 


1-6 


.__ M/M© 1 
LOb UL© Ipg 






• L 


- 


1-2 




o , 


/% 




"" 


0-8 










- 


04 


• / 








- 


0-0 


• / 








- 


-0-4 


/ • 
i i 


l. 


i 


LOG M/M© 
I I 


- 



52 The mass/ luminosity relationship for globular 
clusters in galaxies and systems of galaxies. 
The cause of this relationship is unknown. 



151 



3 5 



11 



13 



15 17 



mass of the Galaxy comes out at something like 140,000,000.000 
times that of the Sun. 

II" the major axis of the image of a galaxy is placed along the 
slit of a spectrograph, the rotational velocity can be found from 
the Doppler effect. Once the distance of the galaxy is known, the 
mass can then be calculated. More than 30 galaxies (including our 
own) have been studied in this way. Among the thirty listed in 
table II, are 19 spirals. 5 barred spirals, 4 ellipticals, I D-galaxy 
(strong radio source) and one peculiar galaxy (a member of a 
double-galaxy system). 

From the table, it is seen that the masses of galaxies range 
between several thousand million limes that of the Sun up to 
several hundred thousand million solar masses. The ratio (m*/L*) 
between mass and intrinsic brightness, expressed in units of solar 
mass, differs between the spirals and the ellipticals. For spirals, the 
ratio lies between 0-7 and 10, with a mean value of about 4, 
while for the ellipticals the ratio is about 12, Mass for mass, the 
spirals are more luminous than the elliptical galaxies. 

The values given in table 1 1 are not definitive, because they 
depend entirely upon the distance estimates, which are by no 
means certain, even though they are of the right order. 

If distance is determined by the distance modulus, the calculated 
mass is proportional to the distance and the luminosity is pro- 
portional to the square of the distance; the ratio mass luminosity 
is proportional to the inverse square of the distance, as given by 
(m/L)ar-"*. If distance is determined by means of the Hubble- 
Humason law. the calculated mass is inversely proportional to 
Hubble's constant and the luminosity is proportional to the inverse 
square of thai constant, while the velocity of recession may be 
expressed as V (recession) = Hr. This gives m(l/H). L (I/H a ), and 
(m/L)H. H. of course, is Hubble's constant. 

The mass/luminostty relation 

Systems which are poor in interstellar absorbing matter make up 



152 



what may be regarded as a homogeneous group. The late Walter 
Baadc classified stars in these systems as belonging to Population 
11. It is notable that the systems include an abnormally large 
number of faint blue stars. 

It is remarkable to find a relation between the colours of these 
Population II systems and their intrinsic brightness, with the bluer 
systems being the less luminous. Moreover, in examining the 
sequence of objects starting with globular clusters (M92 and M3. 
for example), and continued through elliptical galaxies (such as 
M32 and NGC 3379) ending with the galaxies in the Coma 
cluster, to be described below, it is found that though luminosity 
increases regularly according to mass, it does so less rapidly than 
might be expected. The relation between mass and luminosity is 
as follows: 

(L/LO) = (m/310 5 mO) ' 53 . 3 x I0 6 

Another notable feature is the regular decrease in the mean 
density of the systems from the globular clusters through to the 
cluster of galaxies in Coma. Probably this is associated with a 
regular change in the conditions under which stars are formed, 
the masses of the individual newly-formed stars increasing while 
their density becomes less. All this indicates that in the Coma 
cluster there must still be great quantities of gas which have not 
condensed into galaxies. (More about this will be said later.) Also, 
the existence of this relationship casts some doubt on our methods 
of rinding the mean density of matter in the universe, which is an 
important problem in cosmology. 



The formation of spiral galaxies 

In our Galaxy, the older objects move out to great distances from 
the main plane, while the younger objects tend to lie much closer 
to the plane. The flattening of the original star-forming material 
toward the equatorial plane must have taken place so quickly that 
it may be regarded as a collapse process. It is important to find out 



153 



whether the same sort of thing has happened in other spirals, and 
fortunately this can be done, by virtue of the important mechanical 
property of" matter known as the conservation of angular momentum. 

Momentum is the produce of mass and velocity. With circular 
motion, the product of the amount of movement and the distance 
from the axis of rotation is known as the angular momentum. If 
there are no external forces to be considered, and the mass is 
constant, the angular momentum must also be constant; in other 
words, angular momentum is constant in an isolated system. 
Imagine, for example, a body which may be regarded as a point, 
attached to a light string and moving in a circle with uniform 
velocity. If the length of the string is halved, the speed of the 
moving body will be doubled; if the length of the siring is doubled, 
the velocity is halved. 

Studying the movements in a spiral galaxy make it possible to 
calculate the value of angular momentum contained in a cylindrical 
ring of radius r and thickness of one centimetre. We are, in fact, 
considering star-forming material which is originally diffused 
through a spheroidal volume, and rotating with uniform circular 
movement; and this sounds reasonable enough, since star-forming 
material is gaseous and subject to violent turbulence. The viscosity 
of the turbulent motion will be sufficient to make the rotation 
become uniform, as would happen in the case of a solid. And if the 
nebulosity is not in equilibrium, there is nothing to prevent its 
collapse toward the equatorial plane. 

The amount of angular momentum contained in a nebulous 
cloud in the form of a cylindrical ring of radius r and one centi- 
metre thickness can be calculated, and the measured angular 
momentum in a galaxy can be compared with the calculated 
angular momentum in a nebulosity which is rotating uniformly. 
With seven spirals, it has been found that the two quantities are 
equal, within the limits of errors of measurement. As with our 
Galaxy, it seems then that angular momentum is conserved during 
the collapse of a nebulous cloud into a spiral shape. 



154 



155 



Spiral structure 

Observations of spiral galaxies show that objects of different kinds 
contribute to the spiral arms. Photography makes it clear that 
these objects are luminous blue stars together with dark and bright 
nebulosities. In our Galaxy and the Andromeda Spiral, radio 
studies at a wavelength of 21 centimetres have led to the discovery 
of the positions of neutral hydrogen clouds in the spiral arms. In 
our Galaxy, in the neighbourhood of the Sun. it seems that the 
arms are trailing with respect to the general rotation of the system. 

The fact that spiral galaxies are flatter than ellipticals has long 
I en i support to the view that the differences between the two types 
are due mainly to the different speeds of rotation. Yet this cannot 
be the whole story, because elliptical galaxies contain little of the 
dust and gas which is so abundant in the barred and normal spirals. 

The formation of spiral amis is certainly linked with the distribu- 
tion of the nebulous material in space, because the very luminous 
blue stars characteristic of the arms cannot be more than ten 
million years old. This must be compared with the lime taken for 
the stars to be dispersed through the galaxy and with the time 
during which the arms have persisted; there seems no doubt that 
the internal movements in the arms mean that the spiral arms 
themselves must last for something like one hundred million years. 

[hough the origin of the spiral arms is undoubtedly associated 
with the properties of the motion of nebulous material inside the 
galaxies, there are difficult problems to be raised concerning the 
way in which gas condenses by virtue of gravitation, the origins of 
the stars (which then no longer share the motions of the clouds), 
and the magnetic field. The whole question is so complex that at the 
moment we must confess that we do not understand it, and as yet 
there is no satisfactory theory by which the different forms of 
spirals can be classified. All that can be done is to use the straight- 
forward classification given at the start of the present chapter, and 
to continue the search for correlations and relationships between 
theory and observation. 



! 



Elliptical galaxies 

Unlike the spirals, the elliptical galaxies have small angular 
momentum, which explains why they are not markedly flattened. 
And while the essential feature of spirals is their overall rotation, 
the general movement of an elliptical galaxy is slight; the essential 
characteristic is the movement of the stars in all directions, rather 
in the fashion of the molecules in a gas. There are strong analogies 
between studies of elliptical galaxies and of globular clusters. The 
same fundamental principles of mechanics are applicable to each. 

The vi rial 

The sum of the potential energy and twice the kinetic energy of a 
system is called the virial. With a system in equilibrium, the virial 
is zero. The simplest case involves a double system in which the 
movement is circular and uniform, so that the distance between the 
two components never changes. The virial is zero because the 
centrifugal force is equal to the force of attraction. And since a 
system containing a large number of stars may be regarded as being 
in a state of equilibrium, its virial, too, is zero. 

When the radial velocities of the objects in a system are measured. 
the kinetic energy per unit mass can be calculated. The kinetic 
energy of the whole system is equal to the product or its mass by 
the kinetic energy per unit mass. Moreover, the potential energy is 
proportional to the square of the mass and inversely proportional 
to the radius of the system. The radius can be measured, and 
by applying the virial theorem the mass of the system can be 
found. 

This method has been used for three galaxies; Messier 32. 
NGC 3379. and the nucleus of Messier 31 (the Andromeda Spiral). 
The mean velocity of the stars was determined by measurements 
of the spectra of the galaxies, because the individual motions of the 
star cause broadening of the spectral lines due to combined 
Doppler effects. 



156 



157 



Table 1 2 Relaxation times for clusters and elliptical galaxies 



Mass 



Radius (parsecs) 



10 6 100 

10 s 1,000 

10' * 10.000 



Relaxation time 

(thousands of millions of years) 

40 

200,000 
1 60,000.000 



Table 1 3 Masses of clusters of galaxies and of individual 
galaxies in clusters 

Mean radial Number of Mass of Massof 



Cluster 


velocity 


galaxies 


cluster 


galaxies 


m'/L 


Hercules 


631 


73 


75,000 


1.000 


120 


Vtrgo 


643 


600 


1.000.000 


2,000 


600 


Coma 


1,010 


670 


1,000.000 


1.600 


370 


Peiseus 


437 


360 


1,000.000 


770 


230 


Cancer 


427 


84 


1.000,000 


830 


300 



Encounters between stars 

The stars in a cluster behave rather like the molecules of a gas. 
There are movements in all directions, with each star going its own 
way, but because the stars are so widely spread out they do not 
interfere with each other. However, over a sufficiently long period 
of time, each star will have its path modified until the whole 
collection of stars is completely mixed; no trace will be left of the 
situation as it used to be when the system came into existence. 
The time required for mixing is called the relaxation lime of the 
system. It increases with the number of stars concerned and with 
the size of the system. 

While the stars can be regarded as moving independently of each 
other, the calculated relaxation times are relatively long. For stars 
with masses equal to that of the Sun. the relaxation times are as 
in table 12. These values mean that elliptical galaxies can 
never attain statistical equilibrium, simply because the individ- 
ual stars take so long to influence each other. The great length 
of the relaxation time does not necessarily mean that the mass 
values obtained by use of the virial theorem are dubious, because 
even though the virial for a stationary system is nil, the theorem 
gives no information about the velocities of the separate stars. 






And even if statistical equilibrium is not attained, the system 
could still be in a static state, which alone is enough to justify 
applying the theorem. 

Statistical equilibrium can be attained even if the stars take part 
in collected or co-ordinated movement instead of moving inde- 
pendently. Moreover, a small number of very massive objects will 
reach equilibrium more quickly than a large number of objects 
with small mass occupying the same volume of space. A group of 
stars moving in a co-ordinated manner behaves like a single object. 
In an elliptical galaxy, then, it is possible that the co-ordinated 
movements of the stars result in a static state being reached 
comparatively quickly. 



Energy of elliptical galaxies 

If the mass/luminosity relationship is taken as being constant for 
all elliptical galaxies, it is possible to calculate the gravitational 
energy and then work out the relation between this energy and the 
mass of the system. There is no need to take the gravitational 
energies of individual stars into account; we are dealing with the 
energy which keeps the stars together in a system. It is found that 



158 



159 



the gravitational energy increases steadily as the 3/2 power of the 
mass. Let us compare, for instance, a galaxy with a mass 10,000 
million times that of the Sun, which has a gravitational energy 
100.000 times that of the Sun, with a galaxy with a mass a million 
million times greater than the Sun*s, which has a gravitational 
energy 100 million times greater than that of the Sun, 

If the mass/luminosity relation for elliptical galaxies is accepted 
as valid, then the gravitational energy holding the stars together in 
the system will increase as the 1-63 power of the mass. This result 
is in good agreement with the law described above. 

The increase of what may be called 'binding energy* with mass 
can be explained on the assumption that elliptical galaxies were 
formed from a hot, contracting cloud of gas. The stars would be 
formed later, inside the proto-galaxy, by condensation of the gas. 
Presumably the shrinking of the proto-galactic gas came to an 
end when radiation could no longer escape from it. The time when 
radiation begins to be trapped gives a relationship between the 
radius of the galaxy and its density, and consequently between the 
radius and the total mass. The calculated 'binding energy' agrees 
remarkably well with the actual binding energy of stars in elliptical 
galaxies. 

And yet the problem of how stars were formed inside the mass of 
the proto-galactic material is not solved in this way. So far as we 
know, it seems that the originally hot, turbulent gas must have 
cooled down because of the random formation of denser regions, 
so that stars could start to form in the cooler regions. The density 
distribution in a present-day galaxy is, to a certain extent, an echo 
of the density distribution in the turbulent gas of the proto-galaxy. 

Clusters of galaxies 

Fifteen large clusters of galaxies have been studied with respect 
to the distribution of individual galaxies within the cluster. Three 
clusters, those in Hercules, Virgo and Coma Berenices, have been 
studied in detail, and the velocities of the separate galaxies inside 









the clusters have also been investigated. 

The regularity of the distribution of galaxies in these clusters 
suggests a condition of equilibrium, and attempts have been made 
to apply the virial theorem so as to obtain the mean value of the 
masses of the galaxies in the clusters. The results are given in table 13. 
It will be noticed from table 13 that the value of the mass/luminosity 
relationship is much higher for the clusters of galaxies than it is for 
measures of the masses of individual galaxies. There are three 
possible explanations for this: 

a The galaxies in a cluster are much more massive than isolated 

galaxies. 

b The galaxies in a cluster are of the same mass as isolated 

galaxies, but the cluster is rich in intergalaclic materia! which is 

completely or virtually invisible. 

c The clusters are not in equilibrium, so that the properties of the 

virial theorem do not apply. 

The first explanation (a) can be rejected out of hand, because 
there is nothing whatsoever to distinguish a galaxy in a cluster from 
a solitary galaxy, but the second idea (b) has more to recommend 
it. In the first place, in a rich cluster of galaxies, such as those in 
Coma, Perseus or Cancer, the distribution of the individual galaxies 
in space follows the same familiar pattern as the molecules of a gas 
tn equilibrium in its own gravitational field. If the velocities of the 
member galaxies do not result from the effects of encounters 
between themselves, but are due to the original state of affairs, then 
the establishment of equilibrium will be roughly equal to the time 
which an object would take to cross the system. For the clusters in 
Coma Perseus and Cancer, the relevant periods are of the order of 
20,000 million years, 50,000 million years and 40,000 million 
years. This means that the Coma cluster may be in equilibrium, and 
also perhaps the Perseus and Cancer clusters. 

In the Coma cluster, there is a distinct segregation between the 
faint and brighter galaxies. The bright galaxies, of greater mass, 
are grouped together in the central part of the cluster, while the 



160 



fainter and less massive galaxies are proportionately more numerous 
at the periphery - just as a light gas in equilibrium in a gravitational 
field will diffuse further than a heavy gas. An arrangement of this 
kind is a clear argument in favour of a state of equilibrium. 

The next step is to explain the difference between the mass as 
observed in the galaxies and the mass calculated by applying the 
properties or the virial. The straightforward answer is to suppose 
that the difference is due to the presence of intergalactic matter. 
The eminent astrophysicist F.Zwicky has shown that the Coma 
cluster acts as an obscuring region, hiding clusters of galaxies 
which are further away from us. The existence of a mass/luminosity 
relationship for elliptical systems which contain no dust, valid for 
globular clusters as well as the cluster of galaxies in Coma, seems 
also to favour the idea that there is a great deal of invisible nebular 
material. 

The third possibility (c), due to V. Ambartsumian of the Soviet 
Union, is that the clusters of galaxies are not in a slate of equilib- 
rium. This idea is based on a comparison with the double and 
multiple galaxies. It is possible to derive masses for the double 
galaxies on theoretical grounds, and the values obtained are in 
good agreement with the values found by studies of the rotations 
or galaxies. However, multiple systems with three or four com- 
ponent galaxies give systematically higher mass values than those 
derived for the double galaxies. From an analogy with multiple 
stars, which are known to be unstable systems, Ambartsumian has 
suggested that multiple galaxies also are unstable systems in the 
process of dissociation. In this case, the observed differences in 
velocity will be greater than those obtaining in a state of equilib- 
rium, and will correspond to escape velocities of one or several 
members of the system. 

Ambartsumian goes on to suggest that the clusters or galaxies 
are themselves in the course of dissociation, and that the observed 
differences in velocity of the separate galaxies are greater than would 
be the case for a system in equilibrium, so that they are nothing 
more than the velocities of dispersion of the clusters into space. 



161 



Quasi-stellar radio sources 

The interpretation of quasars or quasi-stellar radio sources (Qs) 
is a very difficult matter, and as yet our knowledge is very 
incomplete. It has been said, with truth, that the quasars arc the 
most remarkable objects ever discovered. They are often termed 
Qs galaxies, but we cannot be at all sure that they are galaxies in 
the accepted sense or the term. 

A quasar may radiate some 2,500,000 million times more power- 
fully than the Sun ; its lifetime, calculated from the size or the radio 
source, must be of the order of 100,000 years to 1,000.000 years, so 
that during its career it radiates something like 10 52 joules. Most 
of this energy is synchrotron radiation, from high-energy electrons 
which quickly lose this energy simply because they are radiating. 
Therefore, the source must contain high-energy protons (that is, 
cosmic-ray protons) whose energies are at least one hundred times 
greater than those of the electrons. The protons themselves have 
been accelerated by a mechanism whose efficiency, judged from 
studies of cosmic rays, is not greater than 1/100. 

This tremendous quantity of radiation cannot be explained unless 
it is possible to discover a source which is capable of providing 
10 aa joules, and this is no easy matter. It seems that one solution 
is to suppose that the energy is set free by the gravitational collapse 
of an enormous mass. The continuous radiation or a quasar such 
as 3C-48 or 3C-247 appears to come from a mass with a radius of 
about one parsec; such an object would have the gravitational 
energy needed, and the mass itself would be of the order of 100 
thousand million times that of the Sun, Numbers of this sort are so 
rar beyond our everyday experience that they are quite impossible 
to appreciate. 

Indeed, the quasars seem to be so incredible that some astronomers 
have tried to explain them in other ways. One plausible answer is 
that the quasars are not extragalactic at all, but are objects belong- 
ing to the halo of our Galaxy; in this case they would presumably 
have been ejected from the galactic centre with high velocity. 



53 The ring nebula M 57 in Lyra, photographed with the 200-in Hafe reflector at 
Palomar. This is the best example of a planetary nebula - that is. a faint star 
surrounded by an extensive gaseous shell which has been found to be expanding. 
It has been suggested that a planetary nebula may result from the continuous 
ejection of matter during a certain phase of the evolution of the central star, 
M57 is visible with a small telescope, but the central star, as in all planetaries, 
is very faint. 



163 




164 



According to ihis theory, the quasi-stellar sources would be only 
about 25,000 times as luminous as the Sun. and their kinetic 
energy would be of the order of I0 ]9 joules. And yet the energy of 
such an explosion, which would be supposed to have taken place 
in the centre of our Galaxy some hundreds of thousands of years 
ago, would be too low, by at least one order of magnitude, to 
account Tor the observed number of quasars. On the whole, it 
seems more likely that a quasar is a remarkable kind oT elliptical 
galaxy at a tremendous distance from us, but the last word has by 
no means been said. 

Conclusion 

At this point it may be as well to sum up what is known about the 
galaxies, since this is an essential preliminary to an overall study of 
the universe. 

The realm of the galaxies is more complex than that of the stars; 
we have begun to work out the mechanism of stellar evolution, but 
our ideas about the evolution of the galaxies is at best rudimentary, 
and could even be called nonexistent. It is all very well to classify 
galaxies by means of their forms, but it is important not to under- 
estimate the difficulty of classifying objects which show such 
amazing variety. Though Bubble's simple division of galaxies into 
elliptical, spiral and irregular systems is still useful in its way, it is 
not detailed enough for full analysts. Attempts have been made to 
establish intermediate stages between ellipticals and spirals, 
spirals and barred spirals, and spirals and irregulars, but the 
correlation with spectral properties is poor, and it may be wiser to 
complete Hubble* s classification by adding new categories such as 
diffuse galaxies, nebular galaxies and quasi-stellar radio sources. 
In this scheme, the very luminous diffuse galaxies might fill the gap 
between the ellipticals and the quasi-stellar sources. The quasars 
are at least a hundred times more luminous than normal galaxies, 
and certainly represent the most astonishing discovery of the last 
few years. Because they are so luminous, they can be observed out 



165 



to immense distances, and allow us to probe further into space 
than we could otherwise do. 

Studies of individual galaxies and their movements make it 
possible to find out something about the masses of galaxies. 
Remarkably, the mass/luminosity relationship between galaxies is 
more or less constant between one object and another. Taking the 
Sun as being of unit mass and unit luminosity, the mass/luminosity 
relationship for galaxies ranges between I and 20. This gives a 
key to the luminosities of the galaxies, and hence to the average 
density of matter in the universe. 

Unfortunately, the results obtained in this way cannot be taken 
as wholly reliable. So far as double galaxies are concerned, the 
motions are not unlike those of binary stars, and lead to values for 
the masses which agree quite well with the figures obtained by the 
studies of the internal motions, but the agreement is very poor 
with the multiple galaxies, where the derived values are much 
higher. The result may be expressed as follows: If a system is in a 
state of equilibrium, there is a balance between the potential 
energy and the kinetic energy of the system. The kinetic energy 
depends on the masses of the components and the square of their 
velocity, so that if the mutual distances and velocities are known it 
is possible to work out the relationship between potential and 
kinetic energy, which in turn gives the mass. But by comparison 
with the masses of galaxies as found by the rotation method, the 
relative velocities of the individual members of a multiple galaxy 
are loo high for the system to be in equilibrium. Moreover, the 
masses as calculated by the observed velocities are appreciably 
greater than the masses as cafculated from studies of internal 
motions. For clusters of galaxies, the situation is even worse, 
because if the systems are in equilibrium the masses of the individual 
galaxies would have to be enormously greater than their luminosi- 
ties indicate. 

It is all very puzzling, and the answers have not yet been found. 
Either these immense systems arc not in a state of equilibrium, in 
which case they must be about a thousand million years old (an 



54 The great Andromeda Spiral, M31 (NGC224), 
photographed in colour with the 48- in Schmidt telescope 
at Palomar. This spectacular galaxy is only 2,200,000 
light-years from the earth so that it can be examined in detail 
It has been found to be considerably larger than our Galaxy 
and so is the senior member of the Local Group, 



55 Spiral galaxy NGC 7331 in Pegasus, photographed 
with the 200- in Hale reflector at Palomar The spiral 
structure is well shown, but is very difficult to see 
visually because the galaxy is much further away 
lhan the Andromeda Spiral and members of our Local 
Group, It is, however, typical of spirals of this kind. 



167 





168 



idea which involves continuous formation of galaxies throughout 
the universe), or else the very high values calculated for the masses 
are due to significant amounts of invisible material scattered 
between the galaxies in a cluster. This latter idea sounds plausible 
enough in view of the mass/luminosity relationship, but it must 
be added that the significance of this relationship is not yet clear, 
and it may be that, after ail, the clusters of galaxies are not in 
equilibrium. 

Little is known about the evolution of the galaxies. Undoubtedly 
our Galaxy was produced as a result of a gravitational collapse of 
its material toward the main plane, and the distribution of velocities 
in the elliptical galaxies seems to show that the same sort of thing 
has happened there also, but we cannot work out a true evolu- 
tionary sequence; we do not know whether a spiral evolves into an 
elliptical, or vice versa, or whether neither process is valid. However, 
the radio sources show that evolution in the galaxies must take 
place on a grand scale. In some galaxies there may be a succession 
of explosions, causing large quantities of material to be ejected to 
great distances, and so emitting radio waves for periods of hundreds 
of thousands of years. 

In short, enormous masses of the order of one to a hundred 
thousand million limes that of the Sun, the tremendous complexity 
of the galaxies, incontestable proof of some evolutionary sequence, 
and perhaps information about the formation of the universe 
itself - all these are to be found in our studies of the great star- 
systems which we can see in the depths of space. 



5 The universe 



169 



In the previous parts of this book, we have taken a look at the 
various kinds of bodies which are to be found in the universe. The 
most important of these are, of course, the galaxies, which may be 
single, double, multiple, or grouped into huge clusters. Probably 
there are clouds of tenuous intergalactic mailer spread between 
the galaxies, and the whole universe is permeated by high-energy 
cosmic-ray particles (over 10 18 electron-volts), photons and 
neutrinos. 

The overall study of the universe leads on to studies of the dis- 
tribution of the galaxies in space, the mean density of material in 
the universe, and relationships between the matter which makes up 
the galaxies and the more subtle forms of matter such as photons 
and neutrinos. The first step must be to construct some kind of 
map of the nearby galaxies. 



The structure of the inner metagalaxy 

In 1933, Shapley and Ames, in America, published a catalogue of 
all galaxies brighter than the 13th magnitude. The catalogue 
included 1,249 objects, and a map could be compiled without 
difficulty; the result is given here. There are various interesting 
features of ihe map, notably the Virgo cluster; the groupings in 
Coma, Canes Venatici and Ursa Major, which lie close together in 
a band in the northern hemisphere; the southward extension of the 
Virgo cluster in the direction of Centaurus; the cluster in Leo, and 
the groups in the southern hemisphere which seem to form two belts 
of galaxies. The southern hemisphere is markedly deficient in 
galaxies as compared with the northern half of the sky, and there 
are practically no galaxies around galactic longitude 0°. 

It is interesting to compare the distribution of the galaxies 
brighter than magnitude 13 with the distribution of those galaxies 
with radial velocity less than 1,500 km/sec. The diagram given 
here is drawn from the catalogue of Humason, Mayall and 
Sandage; it is very like the map described above, particularly in 
the northern hemisphere. 



56 The distributional galaxies whose 

radial velocities are less than 1 ,500 km/sec 

(after Van Albade). The sky distribution of 

these galaxies in the southern hemisphere 

ts similar to that for bright galaxies, but 

the northern hemisphere distribution is different. 









171 




57 Galaxies brighter than magnitude 

1 3 are not uniformly distributed 

over the sky (after Shapley and Ames). 



173 



180° 



90° 




180° 






270° 



270° 







174 



The genera] impression is of real grouping of galaxies in space, 
with sub-groups occurring inside the main system, and this sort of 
arrangement was studied by the American astronomer Harlow 
Shapley, who coined the term supergalaxy. In a supergalaxy, the 
individual galaxies are grouped in a disc-shaped system with a 
diameter of 15,000.000 parsecs. There is evidence of this in the 
night sky; the disc is marked by a belt of bright galaxies passing 
close to the poles of our Galaxy. There is a second belt in the 
southern hemisphere, passing through the constellation Fornax. 
which might be a second supergalaxy seen from the side. The 
sparse population of the southern part of the supergalaxy may 
be due to the fact that our own Galaxy is well away from the 
centre of the whole system, so that our view is unsymmetrical. 
And according to Gerard de Vaucouleurs, the distribution of 
radial velocities indicates that the supergalaxy is expanding as well 
as rotating differentially. 

Doubts remain, however, as to the reality of this supergalaxy. 
According to Shapley, it would be surprising if a group of about a 
thousand galaxies, spread over a volume of space 30,000,000 light- 
years in diameter, were found to make up a coherent system. 
Moreover, the radio sources do not seem to have the same kind 
of distribution as the galaxies of the Shapley-Ames catalogue, and 
it must be admitted that studies in the radio range give no support 
to the idea of a supergalaxy. 

In addition, the time needed to set up co-ordinated motion 
inside so fast a volume of space is in the order of 10,000 million 
years and, as will be shown later, this is much the same as the 
period during which the expansion of" the universe has been going 
on. We seem to meet with difficulties here. It is hard to believe that 
so immense a system could have been formed so that co-ordinated 
velocities were present from the very beginning; there would be no 
good reason Tor anything of the kind. A local expansion or contrac- 
tion here and there would be quite on the cards, but this is very 
different from a rotation, involving laws of conservation or move- 
ment which could hardly be satisfied. Yet the time which an 



175 



originally un-coordinated system would take to become co- 
ordinated seems incompatible with the time scale of the universe 
as a whole. To sum up: the supergalaxy idea is attractive, and the 
observations of clusters of galaxies give some support to it. but 
up to the prcscnL time it has certainly not been proved. 



More remote regions 

Our knowledge of the more distant parts of the universe has 
grown rapidly during the last few years, and special mention should 
be made of the catalogue published by F.Zwicky, including all 
galaxies down to the 15th magnitude. But studies of still fainter 
galaxies can only be statistical, and depend chiefly upon actual 
counts. Under the direction of the American astronomer Shane, 
the Lick Observatory undertook to count all the galaxies down to 
magnitude 184; great care was taken to make the count complete. 
For fainter galaxies, down to magnitude 21, the only counts are 
those made years ago by Hubble, which cover very small areas, 
and which are of doubtful quality. 

Some idea of the enormity of the task is seen by looking at 
Hubble's relationship between the magnitudes and numbers of 
galaxies: 

log N = 06 (m — Am) — 4-43 

where m is a correction which depends on the red shift in the 
spectrum. Table 14 gives Hubble's estimated numbers of galaxies 
observable in the whole sky. down to various value of magnitude. 
Bearing in mind that there are a thousand million seconds in 30 
years, and that it takes more than a second to identify a galaxy on 
a photographic plate and estimate its magnitude, it is easy to see 
that even the Lick Observatory project of counting galaxies down 
to magnitude 18-4 is a gigantic undertaking. The examination of 
plates bearing images of galaxies down to magnitude 21 can be 
carried out only by automatic methods, and these have yet to be 
developed. 



176 







Table 14 Numbers of galaxies according to Hubble 


Limiting magnitude 


Number of galaxies, N (m) 


18 


1 .650.000 


19 


5,600.000 


20 


1 9.000,000 


21 
22 


57,000,000 


200,000.000 


23 


400,000,000 



Though it is clearly out of the question to make exhaustive 
counts, much could be learned from sample counts made in selected 
regions. This was Hubbie's method, but unfortunately his results 
are now out of date, and no revision has yet been attempted. 

Clusters of galaxies 

The grouping of galaxies is a very general phenomenon, and ranges 
from multiple galaxies through to the great clusters. The tendency 
is well shown on the Lick maps given here. The density curves, 
depending upon the numbers of galaxies per square degree, show 
that tremendous groups occur. However, there are various diffi- 
culties about giving a full analysis, because there are several 
different points to be borne in mind: 

1 Galaxies really do occur in groups, and the number of members 
may range from a mere two up to many thousands. 

2 Within each group there may be galaxies of all kinds; there are 
relatively few brilliant galaxies, and a relatively large number of 
faint ones. 

3 The sizes of the clusters of galaxies are not uniform. 



177 



4 Clusters of galaxies are scattered all through space, and as seen 
from Earth some of the clusters may lie behind others. 

There are two principal ways of showing that clusters of galaxies 
exist. First, some of them are clearly identifiable on photographic 
plates. Secondly, the physical characteristics of the clusters may be 
obtained by detailed statistical analyses of their distribution in the 
sky. 

In 1936, Zwicky began a systematic study of the clusters of 
galaxies, and his work resulted in many new discoveries. Shapley's 
first catalogue had contained 35 clusters, and had been followed 
by Abell's catalogue of dense clusters, containing 2.712 entries. 
Zwicky 's catalogue included several thousands of clusters, and 
he then started to compile maps. He classified the clusters by means 
of their measured velocities of recession, as follows: 



VELOCITY OF RECESSION. 


km/sec 


CLASSIFICATION 




0-15.000 




Near 


(N) 


15,000-30,000 




Moderately distant 


(MD) 


30,000-45,000 




Distant 


(D) 


45.000—60,000 




Very distant 


(VD) 


60,000 and greater 




Extremely distant 


(ED) 



The diagram shows Zwicky's maps for these five classes, in a 
region in Virgo close to the galactic pole. Zwicky himself noted that: 

1 In regions where galactic and tntergalaclic absorption is negli- 
gible, VD and ED clusters are distributed in a fashion which is 
remarkably uniform and random, bearing in mind the selective 
effect due to galactic absorption when the line of sight passes 
close to the galactic plane and so meets with interstellar material. 
From this, Zwicky concluded that there was no evidence that the 
clusters were themselves grouped into clusters of dusters. Zwicky's 
views will be discussed later. 



2 In every region containing dense N clusters, the number of VD 
and ED clusters is lower than might be expected. Zwicky concluded 



178 



4000 
km/s 

2000 



2000 

1000 
2000 

V, 

1000 

2000 

1000 

1000 

500 





"T i i i i J I II I II I I 1 I I l I I 1 I I l l I I I I I 

.m=130-139 i 

r/R, 

- 2- 



m=120-129 « 




-m= 10-0 -10-9 




-m=8 0-9-9 




I I i I I I I I I i t i i i i i i i i i i I i i i i i i 

180° 270° L 0° 90° 180 



1 79 



58 If the distribution shown in figure 57 is interpreted as marking a vast system 
of galaxies in rotation (that is. a supergalaxy), it is possible to give the longitude 
ol an object belonging to the supergalaxy. In a rotating system, the velocity 
observed from any point in the system depends on the longitude and on the 
distances of the objects observed. The galaxies belonging to the supergalaxy 
have been separated according to magnitude intervals (corresponding, broadly 
speaking, to their distances) and their radial velocities have been given as a 
Function of longitude. For the five distance -intervals considered, the theoretical 
curves have been adjusted according to the velocities observed (after de 
Vaucouleurs) . At first sight, the result seems fairly conclusive, and the idea of a 
supergalaxy seems to agree with the aspect shown in figure 57. However, a more 
detailed statistical analysis, taking into account both the different distances of 
objects of i he same apparent, but different absolute, magnitude, and also errors 
in the velocity measures, casts doubts on de Vaucouleurs' result. More research is 
needed into the whole question of a possible supergalaxy. 



that the dense clusters arc rich in intergalactic dust, which would 
absorb the light coming from more remote systems; this was 
particularly so for the Virgo and Coma clusters, and the cloud of 
galaxies in Ursa Major. A map of the clusters in the Ursa Major 
region, in which the clusters are arranged in order of distance, 
shows that remote clusters seem to avoid the areas in which there 
are closer systems. The irregular distribution is also brought out 
in the map of the Corona Borealis region, in which each galaxy is 
represented by a point. 



The tendency to grouping 

Studies of double galaxies give clear indication of the tendency of 
galaxies to form groups, and of the tendency for sub-groups to 
form inside clusters. 

If the galaxies were distributed randomly throughout space, 
there would be cases in which two galaxies would appear close 
together simply because they happened to lie in much the same 
direction as seen from Earth; this does actually happen, and such 
pairs arc called optical pairs. If galaxies between magnitudes 12-1 
and 13 are taken from the Shapley-Ames catalogue, the numbers 



ISO 



Table 15 


Numbers of physical and optical pairs among 
galaxies between magnitudes 1 2*1 and 1 3 
(Shapley-Ames catalogue) 


Separation 

(minutes of arc 


Number of 
) pairs 


Optical pairs 


Physical pairs 


0-4 




35 


1-4 


33-6 


5-9 




35 


5 


30-0 


10-14 




37 


8-6 


284 


15-19 




37 


12-1 


25-9 


20-24 




30 


15-7 


14 3 


25-29 




31 


19-2 


11-8 


30-34 




27 


22 8 


42 


35-39 




33 


264 


66 


40-44 




37 


299 


7-1 


45-49 




31 


33-5 


(-2-5) 


50-54 




37 


37-5 





(-0.5) 



of optical pairs can be listed, and the numbers of the physical 
pairs can then be obtained by simple subtraction. The results are 
given in table 15. Of course, the negative numbers have no 
significance, and their presence in table 15 is due merely to the 
small number of objects in each group. From the table, it is clear 
that the reality of physical pairs cannot be doubted, and when the 
separation is small the vast majority or the pairs are made up of 
galaxies which are physically associated. When the clusters are 
excluded, it is found that the maximum separation for a physical 



181 



Table 1 6 Frequency of systems in N (near) galaxies 




Number of galaxies 


Frequency 


1 


0-47 


2 


24 


3 


16 



E' Numbers of clusters of given component 
population 



Number of 






Number of clusters 


component gala 


xies 




50-79 






1.224 


80-1 29 






383 


1 30-1 99 






68 


200-299 






6 


Over 300 









pair of galaxies is about 225,000 parsecs. 

The method can also be used to find out which of the multiple 
galaxies are optical and which are physical. Disregarding the 
clusters, the results are as in table 16. It seems, therefore, that on an 
average each galaxy has 1-1 companions, but this figure grows 
according to the increasing density of distribution. In the Virgo 
cluster, each galaxy is accompanied by an average of three physically 
associated galaxies, and the mean distance between the components 
of multiple galaxies is 85,000 parsecs. 



59 A map of clusters of galaxies in a certain region 
of the sky (after Zwicky ) . Note the large clusters 
(1 1 h 08m - 29°, 1 1 h 1 3m - 29°) which are 
relatively close and which conceal more distant 
clusters. Mote that these particular areas 
seem to include fewer clusters than other regions. 



183 



W— 







N - 

_ MD 

' lfc**T m ED 




J1-— 



26- 



W—t 



J2° — 



llN m 



I|h20 m tl^OO" 



10 h *0 m 



Large clusters 

Various precautions must be taken in defining what may 
large clusters, because any cluster is bound to be seen in 
direction as other clusters both nearer and more remote, 
not always easy to sort the various clusters out. 

The number of galaxies in a cluster can be defined, in 
conventional manner, by giving the number of galaxies 
than i stated magnitude. Hubble selected 1,682 clusters 



be called 
the same 
and it is 

a purely 
brighter 
from his 



catalogue, and worked out the frequencies of clusters in terms of 
the number of component galaxies included (table 17). In this list, 
all the clusters arc within a distance of 600.000.000 parsecs. so that 
their velocities of recession are below 60,000 km/sec. The centres of 
these clusters do not seem to be distributed at random; in other 
words, there are apparent correlations between the positions of the 
centres of the different clusters in the catalogue. 

Over the total of the regions studied, different methods can be 
used to compare the observed distribution with a completely 
random distribution. Abel! has concluded that all correlation 
between galaxies ceases over distances greater than 40,000 parsecs. 
However, Zwicky, using other procedures, concludes that true 
clusters of galaxies do not exist over distances greater than 20,000 
parsecs. Certainly the statistical analysis is difficult to make exact, 
and to give an idea of what is involved it will be helpful to digress 
for a moment into the theory of probability. 

Statistical methods 

Let us suppose that a certain number of balls is to be distributed at 
random in a certain number of boxes. All we are told is that the 
balls will not be influenced in any way, so that at the end of the 
experiment there may be boxes without a ball inside, or with one. 
two, three or more. The mean frequency is called Poisson's 
frequency. For example, with 2,000 balls and 1,000 boxes, the 
calculated mean numbers are: 



BALLS 


BOXES 


in 


138 


1 


271 


2 


271 


3 


180 


4 


90 


5 


36 


6 


12 


7 and over 


4 



184 



Obviously, if the balls were not independent of each other, the 
frequencies for zero, one, two balls and so on would be completely 
different. If, for example, balls were acceptable only in pairs, no 
box could contain an odd number of balls, and the number of 
empty boxes would be greater. For 1,000 pairs of balls and 1,000 
boxes, the numbers would be calculated as follows: 



BALLS 


BOXES 


in 


368 


1 





2 


368 


3 





4 


184 


5 





6 


61 



It is therefore easy enough to decide whether a given distribution 
of balls in the boxes is random or not. 

This sort of method of analysis has been applied to clusters of 
galaxies. The sky is divided into parts which are equal in area, and 
the number of clusters in each area is counted, to see whether the 
number of areas containing 0. 1, 2 . . . clusters of galaxies is the 
number which would be expected with random distribution. The 
results show conclusively that the clusters of galaxies are not 
independent of each other. 

The selected areas must not be too large or too small, as in such 
cases the grouping of galaxies is masked. With very smalt areas, 
each area would be expected to contain either one galaxy or else 
none at all, while with very large areas the total numbers of galaxies 
would also be large and unwieldy. It is essential to take a happy 
mean for the size of selected areas. Abell has done this, and has 
found that the maximum 'distance for correlation' between 
clusters is 40 million parsecs. 



185 



Mean density 

The mean density of matter in the universe may be estimated from 
studies of the mean number of galaxies per unit volume, and the 
mass/luminosity relationship for galaxies. The number of galaxies 
in any particular volume of space is highly significant, but un- 
fortunately it is not yet known with any great accuracy. Not 
enough is known about the mean number of galaxies per cluster, 
the mean number of clusters per unit volume, the relative numbers 
of clusters of various types, and the mass/luminosity relationship 
for galaxies of different types. 

One way to tackle the problem is to use Hubble's relation, which 
gives the number of galaxies per interval of magnitude. Extrapola- 
tion to fainter magnitudes, as observed in the Virgo cluster, leads 
to an estimate for the luminosity of galaxies per unit volume. 
Adopting the distance values given by Hubble's law, with the 
constant H = 100 kilometres per second per million parsecs, we 
find: 

1=5-1 x l0-»° LO pc-s 

Adopting a mean value for the mass/luminosity relation equal to 
21, as given by the Dutch astronomer Oort in 1958, the mean 
density is: 

p m 7-3 . 10" 31 g/cm- 3 

A second method is to accept the results of statistical analysis of 
clusters of galaxies, giving about I0- ,U galaxies per parsec. Also 
adopting Hubble's values for the distribution of galaxies per 
magnitude, and a value of 20 for the mass/luminosity relationship 
of the galaxies, it is possible to work out the luminosity per cubic 
parsec, keeping the same value for Hubble's constant: 

1=31 . IO«o LOpc-s 

With a mass/luminosity relationship of 20, the mean density 
becomes: 



186 



187 



p — 4-6 . 10-" g/cm- 3 

This result is naturally dependent upon the scale of distances, 
and this scale in turn depends on the value of Hubble's constant. 
If the value of this constant is changed, then the scale of absolute 
magnitude must also change, which affects both the number of 
galaxies per unit volume and the mass/luminosity relationship. 
If Hubble's constant is multiplied by a (for example, from 100 
km/sec per million parsecs to 100« km/sec per million parsecs), 
the density is multiplied by a 2 . 

The two values for the density given here arc of the same order, 
even though they depend upon different methods of investigation. 
However, a value of the order of a fraction of 10 -30 grams per 
cubic centimetre depends entirely upon the value adopted for the 
mass/luminosily relationship of the galaxies. As has been noted. 
very high values for the mass/luminosily relation are found when 
the masses of galaxies in clusters are worked out on the assumption 
that the system is in a stale of equilibrium. These high values have 
been questioned on other grounds, but we cannot quite exclude 
the possibility that the mean density of the universe is 25 times 
greater than the figure quoted above. This would give a result of 
j 0-29 grams/cm -3 . 



Olbers' paradox 

The brightness of a luminous source falls off as the inverse square 
of the distance from the source. According to nineteenth-century 
views, this property could be extrapolated to infinity. It was also 
thought that the stars were uniformly distributed in space through- 
out the universe, and these two ideas led to a famous paradox which 
the German amateur astronomer H. Olbers published in 1826. 

Suppose that there are N stars per unit volume, each of the same 
luminosity L, Divide space into spherical layers, of successive 
thicknesses <5n, fa and so on. In one layer there must be 47ir 2 eSrN 






stars. At the centre of the sphere, each star will seem to shine with 
a brilliance which is inversely proportional to the square of the 
star's distance from the centre; the mean value will be l(Li4nr 2 }. 
Stars in the spherical half-layer of thickness <5r will produce a total 
brightness of (L/4) NcSr. If layer is added to layer, right out to 
infinity, then the total illumination from the central observation 
point must also be infinite. This is obviously not the case, and so 
the next step must be to compare the calculated result with the 
actual brightness of the night sky. The total illumination of the 
night sky is equivalent to 10.000.000 stars of the 10th magnitude. 
and the combined illumination of all the galaxies out to a distance 
of 10,000 million light-years should be equivalent to 12.000 stars of 
the 10th magnitude. If the geometrical properties of space are 
ignored, then in a non-Euclidean universe the contribution of all 
the galaxies out to 10 million million light-years would give a 
luminosity equal to that of the whole night sky. 

The feeble luminosity of matter in the universe can explain the 
small contribution made by the galaxies to the brightness of the 
night sky. but from a logical viewpoint Olbers' two hypotheses 
that light decreases as the inverse square of the distance, and that 
luminous sources are uniformly distributed in the universe lead 
to an absurdity, because they indicate that the sky should be 
infinitely bright, 

Olbers resolved the paradox by introducing the idea that the 
universe contains absorbing matter, and even very slight absorp- 
tion would be sufficient to hide remote objects completely. How- 
ever, according to modern views this is no solution at all, because 
in an infinite universe the absorbing material would have infinite 
thickness; under conditions of equilibrium, the material would 
emit as much radiation as it absorbed, and the end product 
would still be a sky of infinite brightness. 

Olbers' paradox is founded on a few definite assumptions, as 
follows: 
I The mean density-distribution of the stars is constant throughout 

space. 



188 



189 



2 The mean density-distribution of the stars is constant in time. 

3 The mean luminosity of the stars is the same throughout space. 

4 The mean luminosity of the stars is invariable in time. 

5 There are no systematic or co-ordinated movements of the stars. 

6 The laws of geometry as known on Earth are valid throughout 
the universe; in particular, the apparent brightness of a source of 
light decreases as the inverse square of the distance of the 
source. 

7 Physical laws as known on Earth are valid everywhere, even for 
the greatest possible scales. 

In reality, there can be no doubt that Assumption 4 is untenable, 
because the energy reserves of the stars are not infinite. If we 
postulate a galaxy whose whole mass is composed of hydrogen, 
and whose mass/luminosity relationship is 20, the time needed for 
complete exhaustion of the hydrogen will be 200 thousand million 
years. This idea brings in several more points. It is reasonable to 
suppose that the stars in a galaxy can eject materia! which will be 
broken up and used in the formation of new stars, so that fresh 
generations of stars are born from nebulous material sent out from 
the old-generation stars. As has been noted, the newer material will 
differ from the older insofar as chemical composition is concerned. 

Assumption 5 has not been verified. The red shifts in the spectra 
of galaxies are in themselves sufficient to resolve Olbers* paradox, 
because it can be shown that galaxies below magnitude 21 contri- 
bute up to one-half the total luminosity provided by all the 
galaxies - and the total due to all the galaxies amounts to only 
0-3 percent of the brightness of the night sky. 

There is no good reason to think that Assumption 6 is valid; and 
in any case, general relativity shows that the laws of Euclidean 
geometry arc not valid when the scale becomes very large. More 
about this will be said later. 

Neither can Assumption 7 be verified, because the laws of motion 
are altered when the scale is sufficiently great. All in all, it is plain 
that even theories about the luminosity of the night sky can lead 
on to considerations of the universe taken as a whole. 






Radio sources 

Gibers' paradox turns up again with radio sources, with the added 
difficulty that it cannot be resolved by bringing in the red shift, 
For very high frequencies, perhaps even those oT X-rays, the 
intensity of the radiation decreases slowly, proportionally to the 
frequency, to the power — 0-6 to — 0-8: I is proportional to v-p 
(using the previously-accepted values of p). If radio sources which 
are equal in power and are distributed throughout space to infinity 
are not to make an infinitely great contribution to cosmic radio 
noise, then the intensity must decrease more rapidly than the 
inverse of the frequency. Out to a distance of ten thousand million 
light-years, the contribution of all the radio sources should be 
I0~' i! watts per cycle per second up to 400 megacycles, which 
would be ten times the observed contribution from all the discrete 
radio sources. IT the red shift law were valid out to infinity, the 
contribution of all the discrete radio sources out to ten million 
million light-years would be 400 times as great as the flux which 
is actually observed. 

These figures show up the contradictions very well, but there arc 
other facts to be borne in mind. The red shift law cannot really be 
extrapolated so simply, and assumptions 6 and 7. concerning the 
validity of Euclidean geometry and terrestrial physical laws under 
all possible circumstances, must be summarily abandoned. Actually, 
observation does not indicate thai the sources are distributed in 
the way that Euclidean geometry would have us expect. 

The flux received from a source should be proportional to the 
inverse square of the distance, and the number of sources, above a 
certain limit, should be proportional to the cube of the distance, 
and also, therefore, to the —3/2 power of the flux: 

N = cte F-3' 2 

Such a distribution would give an infinite value for the total 
flux, as indicated by Olbers' paradox. Obviously, this does not 
happen. The observed distribution increases less rapidly when the 






190 



+ 50 



+40 



+30 - 



Q -20 1 




191 






+10' 






14.00 

Right ascension 



13.00 



12.00 



11.00 



60 Radio results at 1 80 cm {after Baldwin and Shakeshaft) . The diagram shows 
the radio temperature curves for areas eight degrees square, the grey regions 
indicating more intense radiation. The galaxies in the Shapley-Ames catalogue 
are shown on the same diagram. The increase in flux in the area between 1 0h 
30m and 1 3h is due to the radiation produced by the Galaxy. The intense area 
between 1 2h 30m and 1 4h, and 8° and 27°, is a region of galactic emission. 
The emission area at 1 2h, extending northward away from declination + 1 0°. is 
due to the strong source Cassiopeia A. The less extensive area from 1 2h 30m. 
1 2°. is due to the source Virgo A and the intense region at 1 2h 1 5m to 1 3h. 
1 5° to +5°, may be due to a supergalactic effect. However the existence of a 
supergalaxy can be established only by other observations at other wavelengths. 
Shapley. who coined the term supergalaxy', considers that the only significance 
of this distribution is a perspective effect of a thousand close galaxies seen 
against a background of thousands of millions of more distant galaxies. 



flux decreases, so that the total number of sources corresponds to 
the observed total flux, which is, of course, finite. 

From the cosmo logical point of view, the main interest of the 
radio sources is that they can be detected out to enormous distances. 
More will be said about the observational data in the section of this 
book dealing with models of the universe. 

Cosmic rays 

In the first section, it was noted that cosmic rays cannot be per- 
manent members of our Galaxy. The total flux of cosmic ray 
particles on the Earth's surface is of the order of 0-6 particles per 
square centimetre per second, corresponding to a density of 1 
particle per 50.000 cubic metres. If the density of cosmic ray 
particles is taken to be constant throughout the universe, the 
corresponding density of energy works out to around 1 erg/cm 3 . 
It is well known that Einstein's formula E = mc 2 establishes 
a link between mass and energy. If the energy of cosmic radiation is 
known, its equivalent in terms of mass can be calculated, and is 
found to be approximately 10 -33 grams per cubic centimetre, 
that is to say, about 1/500 of the density of matter as calculated 
from studies of galaxies. 



192 



193 



It is important to find out how long the cosmic-ray particles 
travel through intergalactic space. Modern theories allow us to 
fix a maximum possible value for the density of the gaseous 
material in the universe, and it is known that to stop a particle 
with an energy of a million million electron volts would need 
encounters with 10 32 atoms. If a cosmic-ray particle were to travel 
for a thousand million years without being halted, it would 
certainly encounter less than 100,000 particles per cubic centimetre. 
This enormous number can hardly be found anywhere in inter- 
galactic space, and we must look for another solution. 

If cosmic ray particles cannot be braked by molecules of gas, it 
is worth considering whether they might be slowed down by 
neutrinos or photons. Neutrinos are relatively sparse, with a 
density of only one per 400 cubic metres, but there are about 1,000 
photons per cubic metre; the density of residual atoms cannot be 
greater than one atom per 40 cubic metres. Taking an effective 
section of about I0~ 26 square centimetres, it seems clear that the 
freedom of a cosmic ray particle is limited essentially by photons. 
The free path, or "clearway', is of the order of one hundred 
thousand million light-years. 

Cosmology 

There is no point in giving further discussions about the properties 
of the universe without introducing cosmologica! problems, and, 
after all, cosmology is the science which deals with the universe 
considered as a whole. 

Olbers' paradox, both in its optical and radio sense, means thai 
we have to try to describe the universe in regions which are beyond 
our observable range: we must also bear the quasars closely in 
mind, because their speeds of recession are so staggeringly great. 
There is an immediate problem to be faced, because it is necessary 
to abandon Euclidean geometry and apply, to three-dimensional 
space, ideas which have been borrowed from the properties of two- 
dimensional surfaces. This is not an easy matter, and it is bound 






to cause a certain amount of mental confusion ai first. Cosmology 
sets out to attack the problems of conditions at the limits of the 
universe if we regard the universe as finite, and the conditions at 
infinity if we take the contrary view. New physical concepts are 
needed, and these lead in turn to new theories and new ideas. 

The idea of curvature 

Consider a curve drawn on a plane surface. At each point, it is 
possible to define the tangent to the curve, and the normal to 
this tangent. Two normals close to each other intersect at a point 
which may be taken as the centre of curvature for that particular 
part of the curve. Working from this point as a centre, a circle can 
be drawn which just touches the curve and which, at the point of 
contact, is very like the curve itself. The distance from the centre 
of curvature to the tangent is the radius of the circle, and is called 
the radius of curvature of the curve at this particular point. The 
radius of curvature is, of course, constant at every point on a circle. 

Next, consider a surface within a three-dimensional space. 
Creatures living on the surface would regard it as a two-dimen- 
sional space. An infinite number of curves may pass through any 
two points of a surface, but. generally speaking, one of these is 
bound to be the shortest possible curve; it is known as the geodesic 
of the surface. The geodesies of planes arc straight lines, in keeping 
with the famous definition of a straight line as being the shortest 
distance between two points. Geodesies are simply extensions of 
this principle; for example, the geodesies oT spherical surfaces are 
great circles. Only one great circle can be drawn through two given 
points of such a spherical surface, unless the two points arc at 
opposite ends of a diameter, in which case, the number of great 
circles that can be drawn through the two points is infinite. 

An infinite number of geodesies can pass through any one point. 
When considering tangents to geodesies, we are able to choose two 
geodesies whose tangents are at right angles to each other, and 
hence to define two geodesies which cut each other at right angles. 



61 Equal -density contours in galaxies 
(after Shane era/). Note I he contours 
which show density peaks, due to 
the presence of clusters of galaxies. 




!8 r 



0* 330° +10° 



17 r 



16" 



310° +30* 



15' 






195 




280° 270* 260° 250* 



14 r 



13 r 



12 h 



196 



A normal plane can describe an arc of a curve on a surface. This 
curve will have a radius of curvature and a centre of curvature. 
If the plane rotates continuously around the normal, it will cut 
off different arcs of the curve, and the curvature will be different 
in each case. In general, the centre of curvature will occupy two 
extreme positions at right angles to the normal plane, and these 
two extreme positions define the two principal radii of curvature of 
the surface. Clearly, there will be a difference between surfaces 
such as spheres, for which both the two principal radii of curvature 
have the same sign, and hyperboloids, for which the principal 
radii of curvature have opposite signs. 

The sphere is a special surface for which the two radii of curva- 
ture are equal at all points of the surface. It is a closed surface, and 
is also a surface of positive curvature. The hypcrboloid, on the other 
hand, is a surface of negative curvature. Following the great nine- 
teenth-century mathematician Gauss, we can define a scalar 
curvature, equal to the inverse of the product of the principal radii 
of curvature. 

Geometry on a surface 

The ordinary principles of plane geometry can be adapted for 
geometry on a surface. Replacing straight lines by geodesies 
means that triangles, quadrilaterals and equal lengths can be 
drawn, and the idea of a circle can be generalised by considering 
the figure obtained when equal segments of the geodesic are laid off. 
starting from one definite point. 

Let us lake the sphere, for example. If equal arcs of great circles 
are drawn, starting from a set point, the resulting points give us a 
circle. This circle is a small circle on the sphere, and it is at once 
clear that for this small circle, the ratio of the circumference to the 
radius is less than In. When the 'radius' is increased, the ratio 
becomes less. When the "radius' amounts to one-quarter of a great 
circle, the "circle' becomes the equator of the sphere, and the ratio 
of perimeter to radius is 4. again less than 2n. When the 'radius' is 



62 Two planes AB. A'B' passing through 
the normal PN cut two curves K. K' 
on a surface. The centres of curvature 
are respectively C and C. 



197 




63 From point P there are arcs of equally 
great circles PA, PB, etc. or PA'. PES', etc. 
The extremities of the arcs of the great 
circles describe a small circle C, C*. etc, for 
which the ratio of the circumference 
to the 'radius' PA is less than 2jz. 




64 Tracing a 'rectangle' on a sphere. 
The 'rectangle' is made up of arcs 
of great circles, as described in 
the text, but the 'rectangle' is not 
closed because point E does not 
fall on top of point A. 



199 




^ 



65 Tracing a 'rectangle' on a hyperbolic surface. 




hall' a great circle, the 'circle* is reduced to the pole opposite to its 
centre and the ratio of the perimeter lo the "radius* becomes 
zero. On a sphere, the ratio of the perimeter of a circle to its 
radius must always be less than 2n. 

Another experiment with regard to the curvature of a sphere is 
to draw a 'rectangle' or a 'square' on it. Mark off a small arc AB 
on the great circle of a sphere, and then try to draw an arc BC 
equal in length to AB and at right angles to it; continue with 
similar arcs CD and DE and it will be found that point E does 
not coincide with point A, In fact, it is impossible to construct a 
'rectangle" made up of segments of geodesies which arc per- 
pendicular to each other. The distance between points E and A is 
due upon the curvature of the surface, and becomes greater when 
the lengths of the sides of the "rectangle" or 'square' are increased. 

On a hyperbolic surface (such as the relief of a mountain in the 
neighbourhood of a pass), the ratio between the perimeter and 
radius of a circle is always greater than 2n, On a sphere, the sum of 
the angles of a 'triangle' is always greater than two right angles, 
but on a hyperbolic surface the sum of the angles of a 'triangle' 
must always be less than two right angles. 



201 



In theory, it would be possible to work out the form of a hill by 
drawing geodesies and "rectangles' in it. by analysing the ways in 
which the rectangles failed to close; it would be possible to estimate 
the curvature of the hill, whether the observer happened to be 
near the summit or in the pass below. Geometers living in a 
permanent fog, and unable lo see the shape of their mountain. 
could nevertheless find out its exact form simply by drawing 
mutually perpendicular geodesies on the ground. 



Geometry in space 

In the neighbourhood of the Earth, the geometry of space is to all 
intents and purposes Euclidean. The great mathematician Gauss 
was able to show that even with a very large triangle, with sides 
about 100 kilometres long, the sum of the angles is equal to two 
right angles. And yet there is no a priori reason to believe that 
when immense distances are involved, space remains Euclidean. 
In other words, if an attempt were made to trace our 'rectangles' in 
space, the rectangles would not close; the sum of the angles of a 
triangle would not be equal to two right angles, and the ratio of 
circumference to radius would not be equal to 2x. The idea of there 
being a shortest distance between any two points must of course 
be retained, but because the 'rectangles' do not close it must be 
said that space is curved. 

The essential aim of general relativity is to link the geometrical 
properties of space with the distribution of matter in space. In 
relativity, the shortest distance between any two points is the path 
which would be followed by a ray of light, so that light-rays in 
space always follow geodesies. 

The three proofs of relativity 

Relativity is a new theory of gravitation, which relates the proper- 
ties of matter to the geometrical properties of space. In relativity, 
gravitation is propagated through space with a finite velocity; the 



202 



Table 18 Schwarzschild's singularity 






Radius of 




Mass 


Schwarzschild 




(Sun=1) 


singularity (km) 


Mean density 


1 


3 


18 x 10" 


100 


300 


1-8x 10" 


10.000 


30.000 


1 8x 10* 


1 .000.000 


4-3 solaf radii 


1-8x10* 


100.000,000 


430 solar radii 


' 8 



velocity of light. The theory also sides with Descartes against 
Newton, in that it affirms that there is no action at a distance. Three 
observational proofs of the truth of relativity theory have so far 
been found, and these are so important that they must be described 
in some detail. 

1 Close to the Sun, space no longer obeys the Euclidean laws, and 
geodesies are not straight lines. As soon as Einstein's general 
theory of relativity was published, scientists started casting around 
for observational proofs, and the obvious one concerned the 
apparent positions of stars very near the Sun in the sky. If it were 
possible to measure the position of a star first when well away from 
the Sun. and then when almost behind the Sun. the difference ought 
to show up; the light-rays would be deviated, because when passing 
near the Sun their paths would not be straight lines. The main 
difficulty is that the stars cannot normally be observed in broad 
daylight, but during a total solar eclipse the sky becomes dark, and 
stars close to the Sun can be photographed. This was done at the 
total eclipse of 1919. When the measured star-positions were 
compared with the positions on a photographic plate taken six 



203 



months later, when the Sun was out of the way, the expected 
differences were duly found, and this was a real triumph for 
relativity theory. When light-rays pass near the Sun, they are 
slightly curved. The maximum deviation is 1-7 seconds of arc. 

2 If a photon is to be taken out of a gravitational field, a certain 
amount of work must be done, and this work comes from the 
energy of the photon, with a consequent increase in the photon's 
wavelength. In fact, the result is a gravitational shift of the photon 
toward the red end of the electromagnetic spectrum. The shift is 
slight; expressed in the same way as a Doppler red shift effect, its 
value at the surface of the Sun would amount to only 0-6 kilo- 
metres per second, which means that it can be measured, but with 
considerable difficulty. At the surface of a white dwarf star the 
value can go up to 20 kilometres per second, which can be measured 
with relative ease. 

3 From the viewpoint of an observer situated at a great distance, 
the Sun's gravitation, in an Euclidean system, differs slightly from 
the field as laid down by Newton's law (that is to say, gravity falls 
off as ihe inverse square of the distance). The difference modifies 
the movements of the planets to some extent; the effect is most 
noticeable for Mercury, whose perihelion advances by 43 seconds 
of arc per century. The effect was discovered in the nineteenth 
century by the French astronomer U.J.J. le Verrier, though it 
was not explained until much more recent times. 



Schwarzschild's singularity 

The curvature of the paths of light rays in the neighbourhood of 
the Sun is very slight, but only because the energy of the Sun's 
gravitational field is extremely weak. If the mass of the Sun could 
be concentrated into a sphere of very small radius, the resulting 
curvature of space would become much greater; and if the mass of 
the Sun could be concentrated into a sphere of radius 3 kilometres, 



204 



light could not leave the object, but would move on the surface in a 
circular path. Therefore, it seems that a star of solar mass but with 
a radius of only 3 kilometres must be invisible; no ray of light 
could leave it or reach it. simply because of its tremendous gravita- 
tion. 

Table 18 gives the radius and mean density of such invisible 
spheres, as a function of their mass. The radius of the boundary 
inside which the material becomes invisible is called Schwarzchild's 
singularity in honour of K. Schwarzschild. the famous physicist and 
mathematician who discovered it. 

Collapse or explosion ? 

As so often happens nowadays, it is found that studies of quasars 
are significant in researches of this kind. The total energy of a 
quasar may be as much as I0 M or 10 63 ergs, and it has seemed to 
cosmologists that the only means of liberating energy upon this 
grand scale is by the gravitational collapse of very massive bodies. 
Very roughly, the energy available would be of the order of the 
product of the mass by the square of the velocity of light, and it 
follows that the collapse of a body or about 100.000,000 times the 
mass of the Sun would release enough energy to explain the 
quasars. The question of collapse also turns up in investigations 
into the evolution of the stars. Under certain conditions, a star with 
a mass more than three times as great as the Sun's can apparently 
undergo indefinite contraction. When its radius has shrunk to the 
value of the Schwarzschild singularity, the star ought therefore to 
disappear. 

When a mass lies within the Schwarzschild singularity, the pro- 
perties of light which have been described earlier in this section 
result in several paradoxes involving collapse or explosion. A mass 
of material in the process of collapse under its own weight remains 
visible as long as light can escape from it, that is to say, while the 
radius remains greater than the value for Schwarzschi Id's singularity. 
The movement of the material and the movement of the light are in 



205 



opposite directions, since the material is moving toward the centre 
and the light is travelling outward from the centre. An observer 
situated well away from the body will see that when the radius 
reaches the Schwarzschild value, the object will vanish. The paradox 
arises because for this outside observer, the body will take an 
infinite time to disappear. 

If the sense of time is reversed, it seems that we appear to be 
dealing with an explosion, but the description as given above is no 
longer valid, because so far as the outside observer is concerned, 
both material and light will be moving in the same direction, that 
is, away from the centre. Therefore, our external observer would 
presumably see an exploding object emerge from the Schwarzschild 
singularity in a finite time. This corresponds more or less to an 
idea of Jordan, reconsidered recently by Neeman and by Novikov, 
in order to explain the eruptions of quasars. 



Singlegalaxies 

Ambartsumian has recently pointed out thai all the single galaxies, 
radio galaxies and even our own Galaxy give indications of 
explosions, or at least expansion of material. In his view, there is 
little justification for the idea that these phenomena should be 
linked with the energy gained by the original contraction, even if 
gravitational energy were liberated during the course of this 
contraction. For this reason, it is unwise to disregard the theory that 
the quasi-stellar sources arc caused by large masses of material 
emerging from the Schwarzschild singularity. Such masses could 
have a slowed-down expansion, as will be described later in this 
section. 

An extra reason for trying to explain the quasars in this way is 
that when gravitational contraction is in progress, the binding 
energy of atomic nuclei is by no means negligible. On balance, it is 
not certain that contraction makes a major contribution to the 
amount of energy available, which is a significant point. Moreover, 
the paradox described above seems to show that so far as an 



206 



external observer is concerned, an explosion out of the Schwarzs- 
child singularity would necessarily occur in a finite time. 

The curvature of space 

The properties of 3-dimensionaI and 4-dimensiortal space are 
naturally more complex than those of 2-dimensional space (that is to 
say, surfaces). The properties of the curvature of a surface arc deter- 
mined by a single quantity, Gaussian curvature. The properties of 
3-dimensional space are determined by six components, which may 
be reduced to three independent quantities; the properties of the 
curvature of 4-dimensional space are determined by no less than 
twenty components, which may be reduced to fourteen independent 
quantities. 

However, for a medium which is homogeneous, that is to say, 
which has the same properties at every point, the number of con- 
stants needed to determine the properties of the curvature is reduced 
to 1, as in the case of surfaces. If this constant is positive, then 
3-dimensional space has a constant positive curvature, and has 
properties analogous to those of a sphere; if the curvature is 
negative, then 3-dimenstonal space will have constant negative 
curvature, and its properties will be analogous to those of a 
hypcrboloid. 

Obviously, it is much more difficult to visualise the properties of 
curved space than to picture the properties of a sphere, but some 
idea of what is meant can be given by considering the properties 
of a sphere in curved space with a constant positive curvature. It is 
assumed that the sphere has been constructed by drawing geodesies 
of equal length in all directions. When the radius of the sphere is 
small, the ratio of the surface to the square of the radius is An, and 
the surface increases with the radius. When the radius reaches a 
value of jtR. where R is the radius of curvature of the space, the 
surface of the sphere reaches its maximum, and the ratio becomes 
(16/n) = 5-1. As the radius continues to grow still further, the 
surface of the sphere starts to shrink, and is finally reduced to a 



207 






point at the opposite pole at a distance JtR. the greatest possible 
distance in the space under consideration. The sphere constructed 
in this fashion fills the entire space, of volume 2ti 2 R 3 . Space with 
constant positive curvature is finite, closed on ilseir, and of finite 
volume; but obviously it has no boundary. 

With space of constant negative curvature, the ratio of the 
surface of the sphere to the square of the radius is equal to 4ji for 
spheres of very small radius, but increases steadily with the growth 
of the radius of the sphere. The volume of the sphere increases 
indefinitely with the increase of the radius, and the volume of 
space with constant negative curvature is infinite. 

Newtonian cosmology 

In Newtonian cosmology the universe is Euclidean; space has no 
curvature, and the properties of light are not linked with the 
properties of matter, as they arc in relativity theory. In other words, 
everything happens as though the velocity of light were infinite; 
there are no limitations on velocities. 

The Euclidean universe - homogeneous, filled with material of 
constant density, and in equilibrium - is not a possibility. To 
explain why this is so, let us consider a homogeneous sphere of 
radius r. The gravity at its surface will be 4/3jrGpr, and this will 
increase proportionately with the radius. For a sphere of infinite 
radius, the surface gravity is infinite. This is a physical impossibility. 
Two answers to the problem may be put forward; one introduces 
the idea of motion in the universe, while the other involves a 
modification of the laws of gravitation. Actually, these two solutions 
are not mutually exclusive. 

An isotropic, homogeneous expansion will remove the difficulties 
facing Newtonian cosmology. At every point, the acceleration due 
to the expansion will exactly compensate the force due to weight. 
In the simplest case, the distance between any two points in the 
universe will increase according to the 2/3 power of the time; in 
this case, the date for the start of the expansion is linked with the 



208 



density of ihc material by the relationship I = (6nGp actual)" 1 , 
and with p actual = 5 x KH 1 g/cm- :i ; the time t works out at 
4 x 10 10 years. The corresponding velocity of expansion is 16 kilo- 
metres per second per megaparsec, or about six times slower than 
the observed velocity of expansion. In other words the energy- 
density of the expansion of this Newtonian universe is about 40 
times greater than the gravitational energy-density. 

The law of gravitation can be modified so as to become a law of 
cosmical gravitation. This involves the introduction of another 
force, cosmical repulsion, which is the opposite of gravitation, and 
increases according to increasing distance. By suitable selection, a 
term of cosmical repulsion can be introduced so that the gravita- 
tional attraction will be exactly balanced, and there is a state of 
equilibrium - but this equilibrium is unstable, and the least per- 
turbation will start the universe in a career of evolution. Increase in 
density means that there will be a catastrophic contraction, while 
a decrease in density will result in unlimited expansion. The reason 
for this is that when density is increased, the force of gravity 
overcomes cosmical repulsion; when the density drops, cosmical 
repulsion becomes more powerful than gravitation. 

The law of gravitation can also be modified by the introduction 
of a gravity-screening term, and this can lead to a static solution. 
This solution has the peculiarity that it is stable with regard to 
every large-scale deformation, as though the gravity-screen masks 
the discrepancy between attraction and repulsion; in other words, 
if the system is originally stable there can be no subsequent general 
expansion or contraction, though there may be small local varia- 
tions. An obvious difficulty facing the static cosmological model 
is its failure to explain the red shift. Instead of supposing that the 
universe is expanding, the theory must introduce a new idea, 
according to which a photon 'ages' and increases its wavelength. 
This would certainly account for the red shift, but so far as we can 
tell there is no justification for introducing a new physical law for 
which there is not the slightest evidence. It seems, therefore, that all 
static models of the universe must be rejected. 



209 



However, two special features of the gravity-screen model are 
worth noting. As has been pointed out by Zwicky, the model 
explains the almost complete absence of clusters of galaxies, and 
this determines the distance out to which the effects of the screen 
make themselves felt - of the order of 20,000,000 light-years. On 
the other hand, if gravitation is explained by introducing another 
elementary particle (the graviton). the law of attraction follows the 
Newtonian law exactly, provided that the graviton has no mass; if 
the graviton is assumed to have mass, then the effect of gravity 
would fall off, with increasing distance, more rapidly than in 
Newton's law. In the graviton theory, the effects of the screen seem 
to be linked directly with the mass of the graviton. It has been 
calculated that if the screen has a range of the order of 20,000,000 
light-years, the graviton would have a mass of 10 -fi2 grams. 

It is true that the idea of photon ageing and the graviton hypo- 
thesis seem somewhat far-fetched, but they cannot be rejected out 
of hand. Moreover, there are many even stranger cosmological 
theories which have been put forward from time to time. 



Einstein's cosmology 

In relativistic cosmology, the geometrical properties of space are 

directly related to the distribution of matter. One of Einstein's 
essential ideas was that gravitation is not merely influenced by the 
distribution of matter, but is determined by it. On this view, it 
seems inadmissible that the solutions of the relativistic equations 
can be determined by conditions of limits; and the best way of 
getting rid of the embarrassment of limit conditions is to remove 
the limits themselves. As the equations gave a static solution only 
for an empty universe. Einstein, in 1916. introduced the cosmical 
repulsion term into his equations, and this led him on to a spherical 
static universe containing matter at a finite density. This universe 
was closed upon itself, finite but unbounded, and seemed very 
satisfactory, because there was no longer any obvious need to be 
bothered about limits. However, it was achieved only by the 



210 



211 



introduction of cosmical repulsion in a form which was admissible 
from a relativistic point of view but unacceptable from the logical 
viewpoint, because it was justified by no physical considerations. 
The cosmical repulsion term had been introduced only so that a 
static solution of the equations could be found, and Einstein later 
rejected the term. 

Note that the radius of curvature of the spherical, static Einstein 
universe would be about 48.000 million tight-years, when the 
density is taken as 5 x 10 -31 grams per cubic centimetre. 

Friedmann's cosmology 

Friedman n was the first to give complete equations for a homo- 
geneous and isotropic universe, and to discuss the various different 
possible solutions. His work was published in two mathematical 
memoirs, the first in 1922 and the second in 1924. He showed that 
Einstein's closed spherical universe must be the only possible static 
universe, because the equations did not allow a static solution for a 
finite universe containing matter at finite density. Above all, 
Friedmann showed that the existence of solutions depended upon 
time. Before the red shifts in the spectra of galaxies had been 
observed, they were to all intents and purposes predicted by 
Friedmann's solutions, according to which the radius of the curva- 
ture of the universe increases in the course of time. 

In particular, Friedmann showed that Einstein's equations, 
without the mysterious cosmical repulsion term, could give many 
solutions, but all of these were non-static; in fact, in relativist ic 
cosmology, as in Newtonian cosmology, there can be no such 
thing as a static-universe model, unless cosmical repulsion is 
brought back. Models in which the universe is assumed to be 
expanding seem to agree much more closely with the observed 
facts. 

The next stage is to look for suitable quantities which may help 
in drawing up a model of the universe. Several quantities are 
accessible to observation: the red shift as a function of distance. 






the number of objects of given kinds which exist as a function of 
distance, and the mean density of matter in space. Only the first 
and last of these quantities are known with any accuracy. Counts 
are unreliable, and diameter measures are of little use unless they 
apply to identical objects. Therefore, the parameters of models of 
the universe are by no means easy to obtain from observation 
alone. 

Consider, for example, a model of the universe in which there is 
no cosmical repulsion. If the model is an open one, the relation 
between Hubble's constant, the density, and the radius of curvature 



is: 



C- ■_,., 8tiG^ 
"K* - H T~ 



If the model is a closed one, the relation becomes: 

C- 8nGp ■_,, 
w = _ 3 H - 

Table 19 gives the values of the radius of curvature as a function 
of the density. H is taken as being 100 km/sec per megaparsec. 
The very small value found for the density strongly suggests that 
the universe is open and infinite. Its radius of curvature (negative 
curvature) is approximately equal to the product of the velocity 
of light by the reciprocal of Hubble's constant, and this seems to 
be due to the great predominance of the density of energy of the 
expansion over the density of the gravitational energy. 



Cosmical acceleration 

There is no a priori reason why Hubble's constant, which defines 
the velocity of expansion of the universe, should be independent of 
lime. A variation in Hubble's constant in the course oT time con- 
stitutes what is known as cosmical acceleration. If this acceleration 
is positive, the rate of expansion will grow steadily as time passes; 
if the acceleration is negative, then the rate of expansion will slow 
down. It is easy to measure cosmical acceleration by means of a 
straightforward magnitude without dimension. To show how this 



212 



Table 19 






Mean density 

(g/cm >> 

6-66 x 10-" 
2x10 " 


Radius of 
curvature 
(thousand million) 
10-3 

128 


Nature of model 

Open space 
(negative curvature) 
Open space 
(negative curvature) 


6x 10 " 


17-9 


Open space 
(negative curvature) 


1 8x10-" 


Infinite 


No curvature 
(Euclidean space) 


54 x 10" 


96 


Closed space 
(positive curvature) 

Closed space 
(positive curvature) 


1-6 x 10-" 


34 



is possible, it will be best lo consider a few examples of simple 
motion : 

1 Uniform motion. Uniform motion is represented by the following 
relationships: 

distance covered z = vt 
velocity i = v 

acceleration 2=0 

Writing H == z/z = 1/t, the acceleration factor is calculated by: 

z 



qo = - 



AV 



= 



For uniform motion, the acceleration factor is zero. 



213 



2 Uniformly accelerated motion. A projectile which is rising 
vertically in the Earth's gravitational field has a uniformly retarded 
motion, while when it falls back to Earth its motion is uniformly 
accelerated. If the starting point in time is taken as the moment 
when the projectile reaches its highest point, and the downward 
direction is taken as positive, we have: 

distance covered: z = }gi 2 
velocity z = v = +gt 

acceleration z = +g 

Velocity can be replaced by the quantity II : H = z/z = 2/t. And 
for the quantity qo = — (z/zH 2 ), we have: qo = — §. So for 
uniformly accelerated motion, the acceleration factor is —\. 

3 Motion of a projectile receding from the Sun. In this case, if the 
velocity is zero when the projectile reaches infinity, the following 
relations are valid : 



distance covered 

velocity 

acceleration 



z = la* 3 

i = v m 2/3 kt-" 18 

/. = 2/9 kf 4 ' 3 



Taking the quantity H = z/z = 2/3 . I/t, the acceleration factor is: 



qo » - 



~zV 



= i 



4 More complex motions. In these cases, the acceleration factor 
depends on the time; it measures the acceleration of the motion from 
a given instant. For example, consider the motion of a projectile. 
If the origin is not taken as the instant when the projectile reaches 
the summit of its trajectory, we find at the initial instant: 

qo = — gZrj/v 2 

where qo measures the acceleration. If the motion is not uniformly 
retarded, and the negative z is ignored, it is seen that qn>0. But 



214 



1 

actual distance in 




/y^" q n =2 


the Universe S 


A 

time 

fc- 



10 - 9-6 -6'6 -4'7 present epoch 



215 



66 Variations in distances between galaxies in different models of the expanding 
universe. The variation of the distance d between two galaxies G , G , (ord mates ) 
is shown as a function of time (abscissa). The same point A represents the 
distance d and the actual instant of the cosmic time for all the models considered, 
The different curves correspond to d i Hereru values of the parameter of 
acceleration. All the models considered here (no cosmological constant) have a 
negative or nil acceleration J in other words, the expansion is slow. The 
properties of the different models represented on the graph can be summed up as : 





Expansion 


Density 


Model of the universe 





regular 


=0 


hyperbolic 


014 


slowed down 


=5-10-3' 
(observed) 


hyperbolic 


1/2 


slowed down 


=1-8 x 10-" 


Euclidean 


2 


slowed down 


=7 2 x 10-" 


spherical 



Note that the spherical closed models with no cosmological constant are models 
of the oscillating universe, while the hyperbolic models are in continual 
expansion. 



when the starting-point for both distance and time is taken as the 
top of the trajectory, we find, as before: qo = — \. 

In cosmology, the variation wilh time of the radius of curvature 
Ro has to be taken into account. Hubble's constant is H = Ro/Ro, 
where Ro is the rate of change of the radius of curvature. Similarly, 
the acceleration Ro is the rate of change of velocity. Expressing 
acceleration by the quantity qo, then q = — Ro/Ro Ho 2 . The 
quantity qo is positive if the motion is retarded, and negative if 
the motion is accelerated. 

For a universe in which the cosmological constant is zero, the 
following relation can be established between the density of matter 
in space and the cosmical acceleration: 



f*> 



3HVj _ . ,_ 
4MG ~~ J0/ 



X 10" 29 g/cm~ 3 q 



If the density po which figures in this relation is really the same 
as that which figures in the expression of the curvature of the 



67 The radial velocity magnitude 
ratio, according to Sandage The 
dots represent observed clusters 
of galaxies , the curves represent 
models of the universe for different 
values of the parameter of acceleration. 



217 



6 



62 



0-8 



0-4 



5 _ 



M 
U 

o 



6 _ 



4-2 



0-8 - 



0-4 _ 



30 



i — i — i — i — i — i — i — T 



i — i — i — i — r 




1_J I i i L_L 



10 



12 



14 



16 



18 



20 



22 



M v -K v 






universe, it follows that : 



JJ m Ho*(2qn - 1) 



Humason, Mayall 
order of qo = 2-5. 
compatible with a 



in which k equals 1, or —1 according to whether the universe is 
closed and Euclidian, or hyperbolic and open. 

The diagram given here gives the shift as a function of magnitude, 
the theoretical relations calculated for different values of the 
acceleration term q , and the points observed. Data due to 
and Sandage seem to give something of the 
but with great uncertainty. Baum's results are 
value for qo between + and 3/2. The lowest 
possible value for q () is zero, corresponding to a hyperbolic universe 
(k = —1). However, the values determined for po seem to cor- 
respond to a density 70 limes greater than the observed value. 
This could be dealt with by choosing a large, negative value for the 
cosmological constant, but unfortunately there is nothing to justify 
a choice of this kind. The value of qo calculated from the density- 
value is of the order of 0-014, which leads to an open hyperbolic 
model but which does not agree with the value found from 
observation. 

Observations of quasars or very blue galaxies ought to clear up 
the uncertainty about cosmical acceleration, because these objects 
are luminous enough to be seen across immense distances. Cer- 
tainly the spectra of the quasi-stellar sources are very different 
from those of other galaxies. Actually, the spectra of quasars seem 
to give a law linking power and frequency. For a law of this kind, 
it is possible to calculate the magnitude correction due to the red 
shiTt, and find a magnitude that has very little dependence on the 
shift. It is then an easy matter to work out what magnitude the 
quasar would have if there were no red shift. By taking the number 
of quasars as a function of their magnitude, there seems a good 
chance of obtaining a relation from which cosmical acceleration 
can be calculated. Clearly, everything depends upon our being able 
to observe quasars out to immense distances. 



68 The193-cm Cassegra in telescope 
at the observatory of 
Haute- Provence, France. 



219 




In America, Sandage undertook an investigation of this kind. 
He used a catalogue containing 8.746 very blue objects, and drew a 
curve giving the number of objects as a function of magnitude. He 
found that down to the 15th magnitude the number of objects 
increased very slowly, but below magnitude 15 the increase was 
much more rapid. Sandage concluded from this that the objects 
down to magnitude 15 belonged to our Galaxy, while the fainter 
objects were quasars. There were enough of the quasars to make 
possible a determination of the cosmical acceleration. It was very 
intriguing to see that the figure for the numbers of very faint, very 
blue objects seemed to be compatible with a value for the constant 
of acceleration qu = 0, though it did not absolutely exclude the 
value for qn = 1 . 

Unfortunately, recent efforts to verify the nature of these very 
blue objects, using a spectrograph, seem to show that only ten 
per cent of them are quasars. Sandage's results can therefore be 
questioned, but in principle his method is sound enough. 

By now well over one hundred quasars have been identified, and 
more will have been tracked down by the time that this book appears 
in print. Eventually, it will certainly be possible to make counts 
which will lead to a much better value for the cosmical acceleration 
term. Certainly we should soon know whether the universe is 
hyperbolic and open (qo ^ 0) or spherical and closed (qo > |). 



Cosmic time 

One of the strongest points of the theory of special relativity is the 
idea that time is relative. Consider an observer at rest, who sees a 
second observer passing by carrying a clock identical with his own. 
He will be able to notice that the second observer's clock is not 
keeping quite the same rale, because in special relativity there is 
no standard of absolute time applicable both to observers al rest 
and to those who are in motion. There is a contraction of the time- 
scale, which decreases with increased velocity. When the velocity 
becomes equal to the velocity of light, the contraction is 'complete' : 



220 



221 



the observer will go from one point to another at the velocity of 
light in zero time, though the observer at rest will record the passing 
of finite time. 

This contraction of the time-scale was the basis of a concept 
described many years ago by Langevin, and known as Langevin's 
paradox. If an observer leaves Earth at a velocity so high that his 
time-scale is 100,000 times slower than that of a terrestrial observer, 
and if he comes back at the same velocity, two years will seem to 
pass by for the moving observer, but the terrestrial observer will 
find that 200,000 years have elapsed. More will be said about this 
paradox later in the present book. 

The time-dilation effect has been experimentally verified by 
studies of the high-energy cosmic ray particles. Some of these 
particles have extremely short lifetimes, of the order of a thousand- 
millionth of a second. However, when they are moving at near the 
velocity of light, their lifetimes appear to be lengthened, tn the 
experimental research, the life-spans of the particles are measured 
by the length of their tracks in the gelatine of a photographic plate; 
the longer the lifetime of the particle, the longer the track in the 
gelatine, and the overall aspect depends on the energy of the 
particle, which in turn is controlled by its velocity. It is found 
that the life-span is greater when the energy of the particle is 
greater, and the relationship between the two factors agrees 
excellently with the predictions of special relativity. 

A more searching analysis of the nature of the time-dilation 
effect shows that, as Einstein said, it is due to the finite value of the 
velocity of light. In the final analysis, two physical systems are taken 
to communicate with each other by means of signals which travel at 
the velocity of light. As with other physical quantities, the rate of 
passage of time in a system depends upon the nature of the system 
itself. 

In general relativity, effects due to motion are added to the 
gravitational effects. Curiously enough, there are some inappro- 
priate logical methods which lead to an accurate result, and explain 
the slowing-down of clocks in a gravitational field. 



I 



A photon has a certain amount of energy, and in view of 
Einstein's famous formula E = mc 2 it is permissible to speak of a 
photon's 'mass'. According to quantum theory, the change of 
potential energy of a photon moving out of a gravitational field 
results in a change of its frequency, and the calculated frequency 
change is in perfect accord with the predictions of general relativity. 
This result can be applied to the Schwarzschild singularity, and 
there is full agreement with the values of the critical radius as 
listed in table 18. Note, in passing, that some authorities have tried 
to explain Langevin's paradox by supposing that an observer who 
experiences acceleration in leaving the Earth will experience the 
same amount of deceleration on the return journey, so that what 
he gains on the swings he will lose on the roundabouts! 

One of the most important results of general relativity is the 
equivalence between inertia! mass and gravitational mass. Because 
of this equivalence, it can be said that when a braking action is 
applied to the projectile in which Langevin's observer is travelling, 
so that the projectile can return to Earth, then everything takes 
place as if the projectile had been placed in a potential gravitative 
field extending from the Earth to the projectile. Under these 
conditions, the paradox is effectively resolved, and the slowing- 
down of clocks in the braking field exactly compensates for the 
time-contraction due to the outward and return motion of the 
projectile. Unfortunately, this interpretation depends on the idea 
that events take place as though an attracting field existed every- 
where between the Earth and the projectile, and this is not valid. 
The projectile is really a rocket; it is slowed down, at least theoretic- 
ally, because it carries its own braking system. From the mechanical 
viewpoint, the Earth does not influence things which take place at a 
distance of several light-years, so that Langevin's paradox remains. 

Obviously, great care is needed in trying to define the relation- 
ships between the local times of two different observers. Logically, 
the relationships can be stated, but in cosmology, a new fact must 
be considered: the unity of the universe. When time is defined 
from one point to another, with reference to the time at a selected 



222 



223 



point, a unique time can be defined for the universe as a whole. 
This unique time can be identified with the local time of observers 
in our Galaxy, and is then called the cosmic time. The evolution 
of the universe, and all the physical variables which are found in the 
universe, can then be described by means of this cosmic time. 

In part 3 it was noted that time can be defined in various ways; 
there is mechanical time as well as energy time, electromagnetic 
radiation time, and radioactivity lime. The fundamental postulate 
is that 'time' as defined by any of these phenomena is always the 
same, so that the chronology of a phenomenon C is the same 
whether it is fixed by the time scale of phenomenon A or by that 
of phenomenon B. 

Ernst Mach, one of the founders of modern mechanical ideas, 
gave a very subtle discussion of the problem of mechanical time. 
He suggested that the inertia of a body is not independent of other 
bodies, so that in effect the inertia of a body ought to be defined 
in terms of the distribution of all the other masses in the universe. 
Mach's idea, taken together with the identity of inertia! mass and 
gravitational mass, means that the distribution of masses in the 
universe ought to fix the law of interaction ; that is to say, it ought to 
determine the value of Newton's constant of gravitation. 

This was the programme that Einstein proposed when, with 
general relativity, he put forward a new theory of gravitation. He 
also noted that his programme had not been fully carried out. The 
law of attraction between bodies remains tied to a fundamental 
constant, and does not depend on the distribution of all the other 
masses in the universe. It is understandable that some physicists 
have considered going back to Mach's idea and Einstein's pro- 
gramme in an effort to work out a new theory of gravitation, in 
which both inertia and attraction would depend on the distribution 
of all the masses in the universe. 

In a homogeneous universe, in which the same properties would 
be valid for every point, the distribution of masses of matter in the 
universe would depend only on cosmic time, so that both inertia and 
the mutual attraction of bodies would also depend upon it. 






Locally, the significance of this would be that the constant of 
universal gravitation would not be a genuine constant at all, but 
would depend upon cosmic time. 

The cosmic horizon 

Red shift increases with distance. In every model of the universe 
there must be a distance beyond which the shift becomes infinite, 
so that wavelengths also become infinite and objects disappear 
from view. The distance at which this happens is called the cosmic 
horizon, and marks the limit of the observable universe. The 
effect applies to a closed spherical universe just as strongly as to a 
universe which is hyperbolic and open. 

The cosmic horizon can be described according to various 
models, and it will be as well to start with our model of the universe 
in which there is no cosmical repulsion. For this model, it can be 
calculated that the line of the cosmic horizon lies at a distance of 
9.530.000.000 light-years. The value of the red shift as a function 
of distance can be calculated, leading Lo the results given in table 
20. The table also shows the apparent wavelengths of the K line 
of calcium, the violet magnesium tine, and the remote ultra-violet 
hydrogen line when corrections to allow for the red shift have been 
made. Data of this kind are of more than academic interest. With 
some of the quasars, the red shifts are great enough to bring the 
normally remote ultra-violet lines down into the visible range. As 
an example, consider one particular quasar which has been identi- 
fied fairly recently. The 2,802 AngstrSm line of magnesium has 
been shifted toward the red as far as 7,500 Angstroms. The ap- 
parent velocity of recession is 510,000 kilometres per second; this 
is not, of course, the real velocity, and in a hyperbolic universe the 
true rate of recession has been worked out at 240.000 kilometres 
per second. This means that the quasar must be about 6,000 million 
light-years away. 

An even more remarkable case is that of the quasar 3C-9, for 
which the red shift is approximately 2. corresponding to an 



224 



225 



Table 20 


Red shift as a function of distance 
(open universe, no cosmical repulsion). 




Distance 

{thousands of 
of tight -years) 


nillions 


Red 
shift 


Apparent waveleng 

K (calcium) Mgll 


th: 

Lyman-a 












3,933 2,802 


1,215 


190 






0-252 


4.900 




3-81 






0-668 


6,520 4,650 




5-72 






1-5 


7,000 


3,300 


7 62 






4-1 




6,190 


9-53 






infinite 







Table 21 Fraction of the universe which is observable 

(spherical universe, H = 100 km/sec/megaparsec 



Density (gm. cm.') 


Observable fraction 


2-4 X 10-" 


0005 


3-6 x 10-" 


018 


7-2 x 10" 


0051 




apparent recessional velocity of 600.000 kilometres per second. On 
the hyperbolic model, all the calculations fix the cosmic horizon at 
a distance of about 9,500,000.000 light-years. 

Even in a closed universe, with a positive curvature, there is a 
limit beyond which no object can be seen. The observable universe 
is a very small pan of the total universe, as shown by table 21 . In 
this table, the extent of the observable universe has been worked out 
according to three different density estimates. It seems thai beyond 
the observable universe there must be still more matter whose 
amount is infinite in the open model, very large in the case of a 
closed universe. One of the features of cosmology is its aim of 
using the properties of visible matter to describe those of matter 
which is invisible and which will, no doubt, remain forever beyond 
our reach. 

Continuous creation 

If wc accept the evidence of the observed density of the universe 
and the value of Hubble's Constant, the universe is about 10,000 
million years old. This does not seem very long in comparison 
with the probable age of our Galaxy and the oldest siar-cluslers 
in the Galaxy, but to suppose that the Galaxy is older than the 
universe is obviously absurd, and somewhere or other there must 
be an error in interpretation. One solution is to suppose that the 
gravitational constant varies over a very long period of lime, but 
a completely different explanation was put forward about 1950 
by H.Bondi, T.Gold and F. Hoyle. all then working at Cambridge 
University. This was the so-called 'perfect cosmological principle', 
involving a steady-state universe. 

According to this theory, there could be no difficulty about very 
great ages. In fact, the time-scale could be pushed back indefinitely, 
since the Cambridge astronomers supposed that the universe has 
existed forever, with the same targe-scale mean density that it has 
today; there was no beginning, and there will be no end. The 
density of the universe considered as a whole never changes, and 



226 



227 



Table 22 Number of galaxies inside a sphere of radius 1 8 
parsecs, as a function of their age (steady-state 
theory). 



Age in thousands of 


Number 


millions of years 




10 


4-2 x 10 4 


20 


2-1 x 10 a 


50 


25 


100 


85 x 10-' 




new matter appears continuously so as to compensate for a decrease 
in density due to the general expansion. The quantity of matter 
created spontaneously in this way is extremely small, of the order 
of the mass of one atom of hydrogen per cubic mclre per ten 
thousand million years, but it would suffice. It was stressed that 
absolutely nothing is known about the form in which matter is 
created, and there can be no physical theories, even tentative in 
nature, to account for such a process. The hypothesis of a steady- 
state universe leads on to the assumption that new galaxies are 
constantly being formed in a universe in which very old systems 
already exist. 

Let us look more closely at the consequences of the "creation" of 
new galaxies in a universe that is expanding. Galaxies "created" at 
any particular epoch are now to be found scattered through a 
volume of space much greater than the volume at the time of their 
creation. With a creation rate of 5 X 10™ 48 grams per cubic centi- 
metre per second, it is possible to calculate the number of galaxies 
of different ages to be found today inside a sphere of radius 100 
million parsecs. The results are given in table 22, The number of 
very old objects to be expected is therefore very low. and such 






objects would be extremely difficult to detect, for nothing is known 
about the evolution of a galaxy over so great a period of time. 

Gold, for example, proposed an explanation for the quasars, 
which he thought to be due to frequent encounters between stars in 
a very old galaxy which had contracted to a small volume, so that 
the component stars would be relatively close together, and 
encounters would be common. However, the time needed for a 
galaxy to evolve to such a state is extremely long, and such an end 
to the evolutionary process would not be consistent with the idea 
of a steady-state universe. 

A possible test would be to find out the ages of the oldest 
galaxies, using methods of the same type as for those for fixing 
the ages of star-clusters, but unfortunately it is not possible to 
estimate the ages of the galaxies at all accurately, so that the tests 
available at the moment are inconclusive. Another test would be 
to study the variation of Bubble's constant over periods of cosmic 
time. With a steady-state universe, the famous quantity qo would 
be not zero, but equal to — 1 ; but, as has been noted earlier, the 
observed value of the parameter q ( i does not seem to be compatible 
with the value of — 1 predicted by the steady-state universe theory. 

Comment about time 

During the course of his investigations on physical subjects, 
Dirac, in 1939. considered a number of dimensionlcss magnitudes 
which were expressed in terms of very large numbers. For example, 
he considered the relation between the electrostatic force of 
attraction between the proton and the electron, and the gravita- 
tional bond between the two particles. The relationship between 
these two forces is of the order of 10 40 . In the same way, Dirac 
noted that the relationship between the radius of curvature of the 
universe and Hubble's constant is also in the region of 10 40 . He 
concluded that because of some new physical principle, the two 
values were the same for some definite reason, and not by sheer 
coincidence, and that because the radius of curvature of the 



228 



universe varied with lime, on account of expansion, the constant 

of universal gravitation must also vary with time. 

This idea was re-examined by Jordan in the years following 
1939, using more refined techniques, and more recently Dicke has 
returned to it. The result has been a new theory in which the 
constant of gravitation really does change over long periods of 
time, and this in turn involves a modification of the fundamental 
principles which give the gravitational equation in general 
relativity. 

The search for proof 

In any cosmological theory, observational proof is naturally of the 
greatest importance. In Jordan's theory, it is assumed that the 
constant of universal gravitation varies with time, and that this 
also applies to certain atomic constants. The immediate result is 
that some other phenomena which depend on the properties of the 
atom would also have to vary with time, in particular, the wave- 
length of the 21 -centimetre hydrogen line. Observations of the 
2 1 -centimetre line are not precise enough to show whether this is 
the case or not, but it certainly seems most improbable. 

Of course, other theories might provide for a variation of the 
gravitational constant without involving any change in the atomic 
constants, and this is what is found in Dicke's hypothesis. Dicke 
set out to discover the effects of a variation in the gravitational 
constant upon various objects whose evolutionary sequences are 
known reasonably well; that is to say, stars in the star-clusters; the 
dynamical evolution or the clusters themselves, and the internal 
structure of the Sun. Tests based upon the dynamical evolution of 
clusters are as yet too uncertain to be of much use, but the study of 
stellar evolution might be more promising. If the evolution of a 
star look place during a steady variation in the gravitational 
constant, the ages of clusters would be quite different from the 
ages usually estimated. 

Using Dicke's theory as a basis, Schwarzschild has studied 



229 



different models of the internal structure of the Sun to try to find 
out just what the effects might be, and il is certainly true that 
classical theory has provided enough information about the age of 
the Sun and the Solar System to make this investigation worth- 
while. Schwarzschild has found that acceptable models of the 
Sun can be constructed allowing for a slow variation of the 
gravitational constant, but a variation proportional to the radius 
of a curvature of the universe would be too rapid for an acceptable 
model to be worked out. 

It is bound to be very difficult to delect a change in the gravita- 
tional constant, even iT it does occur. The only possibility seems 
to be to examine the oldest known objects in the universe, for 
which conventional theories already give plausible estimates; a 
cluster such as Messier 3, for instance, seems to be as much as 
20.000 million years old. The effect of the variation of the gravita- 
tional constant would be to speed up the evolution of the stars, 
so that the new theory would lead to age estimates less than those 
obtained from theories in which the gravitational constant is 
taken to be invariable. One interesting result is that the ages of 
star-clusters would be brought down to below the age of the universe 
as estimated on a scale based upon the period during which ex- 
pansion has been going on. 

ll is dangerous to be misled by seductive results of this kind. 
Theories of stellar evolution lead to results which are qualitatively 
of the highest interest, but all these results are subject to revision, 
and in any case they depend on what we find out in the future 
about the physical phenomena which control the internal structure 
of a star. 

Several revisions of the estimates of cluster-ages have been 
made during the last few years, and there is nothing to prove 
that conventional theories cannot yield results compatible with 
the hypothesis of expansion. 






230 



Nature of the red shift 

Li tile has yet been said so far about the nature of the red shift, 
which is clearly of vital importance in any discussion. A red 
shift is, of course, known in the form of a Doppler effect, when 
a luminous source is moving away from the observer, but general 
relativity adds two extra reddening mechanisms. One of these is 
the reddening of a photon which is leaving the gravitational field 
of a star: the other is an interaction of light with a gravitational 
field, and is associated with the variation of the radius of curvature 
of the universe over a period of time. 

Over the past forty years, F.Zwicky, who has carried out all 
his observations at Mount Wilson and Mount Palomar, has 
questioned the usual interpretation of the red shift, and has 
always proposed the alternative theory according to which a 
photon becomes reddened during its movements in space. Physicists 
have looked critically at this viewpoint, basing their interpretations 
on ordinary quantum theory. Certainly protons moving in space 
may well collide with other photons, electrons, neutrinos or other 
kinds of particles. 

In the so-called Complon effect, the frequency of a photon may 
be altered, and its wavelength lengthened, as a result of an inter- 
action between an X-ray photon and an electron. Therefore it 
seems reasonable enough to suppose that when a photon suffers a 
series of collisions with other particles, its wavelength may be 
increased, which would result in a red shift. Unfortunately there is 
another point to be borne in mind as well as the conservation of 
energy: the momentum (product of mass and velocity) must also 
be conserved. This means that as the photon undergoes its series of 
collisions, it not only suffers a change in wavelength, but is also 
affected by diffusion. It is found thai ihe change in wavelength 
would not only involve a broadening of the spectral lines com- 
parable with the actual change in wavelength, but would also 
make the images diffuse, and this simply does not happen. The 
spectral lines of distant galaxies are no broader than those of 



231 



closer galaxies, and the images are certainly not diffuse. This 
straightforward fact of observation has always been one of the 
main reasons for rejecting Zwicky's interpretation of the red shift. 

Certainly there is no proof that the suggested process occurs in 
nature, and this is a definite weak link in the argument; ycl it does 
not seem reasonable to exclude, a priori, the theory that the red 
shift is due merely to an alteration of photons due to new kinds 
of interactions between photons and other features of the universe. 
In fact, the idea cannot be rejected out of hand. Incidentally, some 
years ago it was believed that in a distant galaxy, the 2 1 -centimetre 
line had been observed to be lengthened in wavelength in the same 
way as the visible lines; but later work showed that this observation 
must be erroneous. When it is claimed that red shift is independent 
of wavelength, all that is really meant is that the shift is independent 
of the wavelength so far as the visible spectrum is concerned. 

The hypothesis of the ageing of photons leads back to a con- 
sideration of the steady-state universe, because it involves re- 
jecting the theory that the density of the matter can change over 
periods of time. This in turn affects all discussions about the 
evolution of the galaxies, and observations of old galaxies. In 
such a theory, it must be agreed not only that fresh galaxies are 
being formed at the present time, but that there is an evolutionary 
process resulting in the destruction of old galaxies. Therefore, the 
number of very old galaxies that can be observed ought to be much 
larger than in the steady-state theory. This is one indication of the 
difficulties that have to be faced in trying to construct a model for 
the universe in which the red shift is due simply to the ageing of 
photons. 



Cosmological tests 

All sorts of models of the universe have been put forward since 
the publication of Einstein's theory of general relativity. In some 
of these, such as Zwicky's, expansion is rejected; Bondi, Gold and 
Hoyle have favoured the steady-state model; Dirac, Jordan and 



232 



233 



Dicke suppose thai the gravitational constant varies with time. 
Few definite conclusions can be reached as yet, but it will be useful 
to look more closely at the possible tests. As a start, we have 
various observed facts : 

1 The red shift of the spectral lines. 

2 The apparent magnitudes of galaxies. 

3 The apparent diameters of galaxies or clusters of galaxies. 

4 The numbers of objects as a function of their characteristics 
(or. to be more precise, counts can be made separately for 
normal galaxies, radio sources and quasars). 

5 The study of radio noise in the 3 to 7 centimetre band, which 
provides information about the temperatures of electrons 
situated at great distances from us. 

Conventionally, a distance may be defined as a quantity such that 
the luminosity falls off" according to the inverse square of the 
distance. To determine this conventional distance, the modifications 
caused by the red shift must be known. This means that the 
distribution of energy in the spectra of the galaxies must be 
measured very accurately; the exact correction due to the red 
shift must be calculated, and the properties of the photographic 
equipment used must also be taken into account. Certainly the 
process is not easy, and there are great difficulties in trying to link 
conventional distance with red shift. So long as the distances remain 
small, the problem can be solved; but in a curved space in a state of 
expansion, the red shift is not exactly proportional to the distance, 
and it may be necessary to see whether terms proportional to the 
square or the cube of the distance should be introduced. In an 
expanding universe, the term proportional to the square of the 
distance is proportional to the acceleration of the expansion, and 
this may help in deciding whether the rate of expansion is acceler- 
ated (positive acceleration) or retarded (negative acceleration). 
One trouble about trying to apply a correction to the magnitude is 
that photometry of galaxies is by no means yet perfect. Still, it 
seems that the expansion is retarded over a time-scale of the order 
of 2,500 million years. In a static universe this quantity would be 






infinite; in an Euclidean universe in which the red shift is attributed 
to the ageing of photons, the expansion would seem to be retarded 
over a time-scale of 10,000 million years. In short, the measured 
values for the retardation do not agree cither with the idea of a 
static universe or with the theory of photon-ageing - and other 
methods of investigation must be sought. 

Recent studies of radio noise in the very short wavelength 
region have led Hoyle and others to reject the steady-state theory. 
The only logical explanation for the intensity of radio emission at 
3 centimetres is that electrons at a very high temperature are 
seen very far away but with such a red shift that they look very cold. 
These electrons represent what we presumably see of the very 
dense universe at the start of the expansion; at that epoch, the 
matter must have been extremely hot. Calculations have actually 
shown that models of expanding universes arc consistent with the 
centimetre-wavelength emissions which are observed. 

It is probably fair to say that by now the steady-state theory, at 
least in its original form, has been abandoned by almost all 
authorities. It was an attractive and plausible idea, but it did not 
fit the facts, and. like many other attractive theories, it has had to 
be given up. This does not mean that the 'big bang* idea is necessarily 
correct, but it does mean that the universe is in some sort of state 
of evolution. 



Quasars 

Quasars, as we have seen, could be remaining 'pockets' of the 
super-dense matter of the universe in its original state; this explana- 
tion is perhaps rather like that accepted by Hoyle when he 
abandoned the steady-stale theory. 

To justify the steady-state theory. Hoyle had previously been led 
to a generalisation of the gravitational equations of general 
relativity; this generalisation could have been interpreted as a 
continuous-creation term. However, a different interpretation is 
more likely, according to which the term would be interpreted as a 



234 



235 



cosmical repulsion term with its value dependent upon the density 
of matter. Under these conditions, there are possible models in 
which the high density is accompanied by a repulsion sufficient to 
allow the model to expand. In these models there arc no singu- 
larities in the past, that is to say, no stages in which all the matter in 
the universe is concentrated into a theoretical point, and Hoyle, with 
his colleague J.V.Narlikar, has described how great masses of 
matter might first contract and then expand again. This oscillation 
of very massive bodies, with a stage of minimum radius, could 
result in the production of quasars. 

Matter and anti-matter 

When Dirac worked out the theory of electrons, in 1 929, he was 
surprised to find electrons with positive energy as well as those with 
negative energy. From the physical viewpoint this result was 
somewhat obscure, and Dicke interpreted these electrons as 
having a charge opposite to those of normal electrons, so that the 
energy must be positive. At that time the idea of a positive electron 
was theoretical only, but it was soon confirmed by actual observa- 
tion; positive electrons were discovered by Anderson. Nowadays 
they are generally known as positrons. 

When an electron and a positron meet, they annihilate each 
other with the production of a gamma-ray, and we have here an 
example of ordinary matter (the electron) meeting what has become 
called anti-matter (the positron). Apart from the photon, all 
elementary particles have their L opposites" as anti-matter; it has 
already been noted that the anti-proton, for instance, was dis- 
covered at Berkeley in 1955. In annihilating each other, the proton 
and the anti-proton give rise either to pairs of particles and anti- 
particles, or else to high-energy gamma-radiation. 

Nothing in modern theories of elementary particles suggests 
the stability of anti-particles is any different from that of ordinary 
particles. The world of anti-particles is just as stable and real as 
the world of particles. H. Alfven has suggested introducing a 









new name, 'koinomatter', for ordinary matter of the kind making 
up our own part of the universe. 

There are two possible hypotheses. According to one, there is a 
real fundamental dissymmetry between particles and anti-particles, 
and our universe is made predominantly of particles simply 
because it is not suited to the formation of anti-particles. Physicists 
are faced with the problem of trying to work out how stability 
could be achieved under such circumstances. On the second 
theory, particles and anti-particles are formed in equal numbers in 
the universe, and various individual regions happen to be made 
up either of ordinary matter or anti-matter simply because of 
chance local conditions. According to the second idea, Klein 
proposes that bodies in the universe are formed under conditions 
of equilibrium and high temperature, and that they are produced 
from a mixture of radiation, particles and anti-particles within 
their own gravitational field. Only the cooling of massive 'mixtures' 
of this sort could result in the formation of actual objects. 

If these initial conditions are accepted, the next step is to see 
how a 'galaxy' of anti-particles could exist inside a universe made 
up of ordinary particles (or koinoparticles. to use Alfven's term). 
Alfven looked critically at this problem, and concluded that 
between a "galaxy' of anti-particles and the universe of particles 
there must be what may be called a frontier zone, where there is an 
extremely energetic source of radiation which repels the particles 
and so separates them from the anti-particles. This layer would 
prevent any catastrophic mixing, and would make encounters 
between matter and anti-matter a very gradual process, Alfven has 
also tried to account for the quasars, which he regards as being 
due to the emission of radiations and particles of tremendous 
energy in a stable frontier zone, where matter and anti-matter 
meet. 

The Soviet chemist Semenov has provided a graphic picture of 
the properties of matter and anti-matter by pointing out that a 
man made up of matter and a woman composed of anti-matter 
could meet in space, exchange signals, know each other and even 



236 



237 



love each oiher, but they could never touch each other! All this 
is highly intriguing; but as yet there is no definite evidence either 
for or against Alfven's theory. 

The question of anti-matter also crops up when we consider the 
steady-state universe. With continuous creation, matter could well 
appear spontaneously together with equal amounts of anti- 
matter. But whether material appeared in the form of neutrons and 
anti-neutrons or of protons and anti-protons, the meeting of a 
particle and an anti-panicle would still be followed by the emission 
of highly penetrative gamma-rays, and it is possible to calculate 
what the flux of gamma-radialion reaching the Earth should be. 
Here an observational check can be made, because the American 
satellite Explorer XI detected gamma-radiation in the neighbour- 
hood or the Earth. Ft seems that the flux is a million times less than 
the flux that would be required by the theory, and so it seems safe 
to say that even if continuous creation is going on. it does not 
involve the production of equal numbers of particles and anti- 
particles. 

The ages of the stars and the universe 

It has already been noted that the ages of star-clusters can be 
estimated, and that studies of radioactive elements lead to at least 
an approximate determination of the epoch at which the clusters 
were formed. The oldest objects are perhaps over 10.000 million 
years in age. and these estimates, rough though they may be, seem 
to agree quite well with the time-scale of 10.000 million years 
deduced from Hubble's constant. Of course, if firm evidence were 
forthcoming that some of the objects in the universe must be older 
than 10,000 million years, the whole questions of the nature of the 
expansion, the red shift, and the structure of the universe would 
have to be critically re-examined. 






The diameters of the clusters of galaxies 

Zwicky suggested that in order to avoid having to correct the 
magnitudes of the clusters of galaxies due to the red shift, it would 
be helpful to count the clusters to draw up a relationship between 
their numbers and ihcir diameters. Assuming that all clusters arc of 
much the same size, and that they spread throughout the whole of 
space, the relationship would be quite a simple one. but would be 
different for an expanding universe than for a static one. 

In theory, this is all very well - the test would be better than one 
involving magnitudes. Unfortunately it introduces the effects of 
observational selection, because very faint clusters would probably 
escape detection altogether; the numbers of clusters of small 
apparent diameter would be too low, and the clusters of large 
diameter, which would certainly be observed, are not numerous 
enough lo provide the data for a reliable statistical analysis. 
Zwicky's curve suggests that there is no expansion, but his numbers 
can be differently interpreted and so made to agree with an expand- 
ing universe. More information is needed before the test can be 
properly carried out. 

Counts of galaxies 

Moreover, Zwicky's hypothesis is over-simplified, because it is 
known that the sizes and populations of different clusters are not 
uniform. Studies of the numbers of galaxies as a function of 
magnitude should, naturally, take heed of the statistical properties 
of the distribution of galaxies in a cluster. As an analogy, let us 
suppose that we are observing a large forest from a distance, and 
that the forest contains trees of all ages, arranged in groups. The 
important factors are first, the number of trees in each group; and 
secondly, the distribution of the trees in different age-groups. 
Straightforward counting of the number of trees should provide 
information about the groups, provided that the law of distribution 
by age-group is known. 



238 



239 



Analogies of this sort show that the general problem is by no 
means simple. And with the galaxies there are many things to be 
taken into account; just as a small, nearby tree could easily be 
confused with a large, distant tree, so a near, faint galaxy is only 
too easy to confuse with a galaxy which is much brighter and much 
further away. To try to find out the space-distribution of galaxies 
from their visible aspect is rather like disregarding the colours of 
leaves which will distinguish a young tree from an old one. Also, 
just as the slope of the ground could affect the statistical analysis in 
the tree example, because the number of trees per unit surface must 
depend upon the slope of the mountain, so the statistics of galaxies 
are bound to be somewhat affected by expansion. However, the 
results obtainable are confined to an area so close to the Earth that 
the effects of expansion would be loo slight to be noticed, and here. 
too, the test is inconclusive. 

Counts made separately for normal galaxies, radio sources and 
quasars seem to be more promising, because the numbers involved 
are fairly large (around 1.200) and because there are some very 
brilliant objects which can be seen across tremendous distances. 
Counts of radio sources, undertaken mainly by Ryle and his 
colleagues at Cambridge, do not support the steady-state theory, 
though it is true that the effects of observational selection are still 
not known as well as might be hoped. 

The Singular State, or the Big Bang 

Homogeneous, isotropic models of the universe all suppose that 
the expansion must have started from a 'singular state' of infinite 
density, pressure and temperature, so that there has been much 
speculation about the physical processes operating at the moment 
of the so-called 'big bang*. Actually, the original singular state 
could be dispensed with if the models arc homogeneous but not 
isotropic, because such models would show "slipping", slipping 
with rotation, or rotation alone. Therefore, the singular state has 
changed its nature, and the density, pressure and temperature need 









not be taken as being infinite. Even a slight departure from isotropy 
is enough to cause a complete change in the character of the 
singular state through which the universe has passed, and the 
departure is even greater when rotation is taken into account. It 
then seems that the initial 'big bang" does not account Tor the 
expansion now in progress. There is no need for the modifications 
of the equations of general relativity, as suggested by Hoyle and 
Narlikar, to avoid a physical singular stale at the cost of the 
expansion. 

This may be a suitable moment to say something further about 
general relativity. In the theory of gravitation, it is not really natural 
to introduce a priori the distribution of matter in space. The more 
natural procedure, as followed by Einstein, Infeld and Hoffman, 
is to suppose that matter acts as though it were a distribution of 
mass-singularities in space, so that there is no need to introduce, 
artificially, a continuous distribution of matter in space; it is 
enough to study the relationships between attracting "singular 
points'. When such a relativistic system is studied to successively 
higher approximations, different properties come to light in 
succession. When the approximations are rough, the material 
singular points are displaced with uniform motion, or, in mechani- 
cal terminology, with Galilean motion. Newton's law of universal 
attraction, and the fundamental dynamical principle according to 
which force is equal to the mass multiplied by acceleration, are 
discovered at the next more refined approximation; and al the 
next approximation still, the first relativistic corrections are found. 
as in the two-body problem corresponding to the advance of the 
perihelion of the planet Mercury, The importance of this analysis 
is that it stresses ihe link between the movements of material 
bodies and the laws of dynamics. Everything hinges upon the bond 
between the singular field of each particle and Ihe fields of all the 
other particles. 

Applying these ideas lo the universe is one of Ihe most im- 
portant tasks of general relativity, and brief mention must be made 
of ihe theory put forward by Pachncr. which is very difficult from a 



240 






241 



technical point of view but which ought certainly to be verified and 
developed. What has been said here should serve to emphasise that 
even in its conventional form, general relativity has by no means 
realised alt its possibilities as yet. 

The universe and cosmogony 

Undoubtedly the present time is a critical one in cosmology. With 
the advances in studies of quasi-stellar radio sources, extraordinarily 
powerful means of sounding the depths of the universe have been 
discovered, and the problem of origins of these sources, a matter of 
vital importance in cosmogony, is closely allied with the cosmohgica! 
problem of the structure of the universe. It is not impossible that 
the whole question is linked with the whole manifestation of the 
material in the universe. 

In any case, studies of quasars should soon be able to provide 
answers to the outstanding riddles concerning the expansion of the 
universe. What has to be done is to probe as far into space as is 
possible, and for this the incredibly brilliant quasars hold out 
much the best hopes. 

Conclusions 

The universe is made up of stars which are grouped together in 
galaxies of innumerable shapes and forms. The average density of 
the material available to observation is very low, of the order of 
three atoms of hydrogen per ten cubic metres, but this material 
makes up objects of enormous complexity. In every direction, as far 
as we can see, there are galaxies of stars. The stars arc formed 
constantly, and go through processes of evolution; the galaxies, 
too. are born, develop and die. But while a great deal has been 
learned about the evolution of the stars, our knowledge of the 
evolution of the galaxies is still depressingly meagre. 

The great galaxies, as luminous as tens of thousands of millions 
of suns, can be seen across distances of thousands of millions of 









light-years. A hundred times brighter still are the quasars, which 
bring us to the limit of that part of the universe which is within our 
observable range. Nuclear sources can account for the energy of 
normal galaxies, but this is not so for the radio galaxies, while the 
quasars must be drawing upon some mysterious energy-supply 
which can give them their tremendous brilliance and also produce 
an abundant flux of particles which seems to resemble the particles 
of cosmic radiation. 

Whether the universe is spherical or hyperbolic, observations of 
the galaxies force us to abandon Euclidean geometry in our efforts 
to understand the strange properties of the curvature of space. 
What is termed Riemannian geometry, not discussed here because 
it is beyond the scope of the present book, has become a physical 
reality instead of nothing more than an abstract mathematical 
hypothesis. But though we may assume that the universe is 
curved, the basic concepts still elude us. The newly-found very 
blue galaxies, the quasi-stellar sources, are so far off that the 
measures made of them are highly relevant in this connection; the 
most remote have red shifts so great that the Lyman-alpha line is 
observed in the blue part of the spectrum. 

Quasi-stellar sources are being discovered at a surprising rate, 
and dozens of them are now known. Their mean absolute magni- 
tude seems to be —24' 7. corresponding to the retarded expansion 
of a closed spherical universe in which the parameter q<i, a measure 
of the retardation, works out at +1. It is quite likely that over 
100,000 quasars above an apparent magnitude 19 exist, and the 
analysis of the very blue objects referred to earlier in part 5 is 
even more interesting, as well as perhaps more deceptive, than it 
appeared to be a year or two ago. Yet counts of them cannot be a 
reliable guide to the properties of cosmological models, and until 
spectroscopic analysis of their light become possible it will be very 
difficult to come to any conclusions about their true nature. Such 
an analysis will be a difficult matter, and will take a long time. On 
the other hand, it has been shown ihat the numbers of very blue 
objects, that is to say, quasi-stellar sources, are very large, and must 



242 



be measured in hundreds of thousands. 

Another observation made comparatively recently may also turn 
out to be fundamental - the detection of background radio emission 
from the sky. The research has been carried out at wavelengths of 
2-4 centimetres, 3-3 to 7 centimetres, and 21 centimetres hy the Bell 
Telephone Company and the Princeton Laboratory; the intensity 
seems to correspond to the thermal agitation of electrons in a 
temperature of 3 degrees absolute. This emission does not corre- 
spond to any known radio sources, and the measures seem to he 
accurate to within 20 per cent. 

According to one interpretation, the electrons of intergalactic 
space are too few in number to contribute appreciably to the 
general background radio emission, even if this were probable 
on other grounds, which it is not. Therefore, the cause lies in some 
very distant source, possibly connected with the primitive state of 
the universe immediately following the start of the expansion; in 
fact, the thermal emission represents the remains of the big bang. 
Efforts have been made to develop as coherent a theory as possible, 
accounting for the background radio emission in the centimetre 
wave-band as well as other known facts. The original expansion 
of a very hot, dense universe presumably took place very rapidly, 
and after some thousands of years led to the residual gas made up 
of cold electrons. This seems to account for the background 
emission, but it may be possible to consider events of an even 
earlier period, and this has led lo some sort of a revival of an old 
theory put forward by Alpher, Bethe and Gamow to explain the 
origin of the various chemical elements. 

When the age of the universe was 1/100 of a second, then, 
according to Alpher and his colleagues, the temperature was of the 
order of 100.000 million degrees centigrade, with a density or 1,000 
grams per cubic centimetre. As rapid cooling took place, different 
kinds of stable nuclei were formed. Calculations can be made for 
the abundance of helium and deuterium at the virtual start of the 
expansion, because we know the present density of the material 
in the universe, and we also know the present abundance of 



243 



helium and deuterium, as well as the temperatures of the electrons 
near the boundary of the observable universe. So far as helium is 
concerned, initial densities of 2 x 10"'*, 7 x 10 -31 and 2 x 10" 32 
grams per cubic centimetre are all compatible with the available 
data. The results for deuterium are much less satisfactory, because 
so much depends upon the mean density of the material in the 
universe; the hypothesis of 2 X 10~ 32 grams per cubic centimetre 
leads to a present abundance for deuterium of about 1 per cent, 
which is about fifty limes too high. A value between 2 x lO" 29 and 
7 x 10 -31 gives much better agreement, but no final conclusions can 
be drawn, because it is known that the material now spread through 
our Galaxy has passed through the stellar state several limes, 
during which periods deuterium must be destroyed in large 
quantities. 

The Solar System is probably less than 5,000 million years old, 
and so is much younger than the Galaxy, whose age is certainly 
10,000 million years and perhaps more. During the 5,000 million 
years which elapsed between the beginning of ihe Galaxy and the 
origin of the Sun. the material may well have been contained partly 
in stars and partly as interstellar matter. Mixing of this sort is 
bound to result in considerable losses of deuterium. It is notable 
that the abundance of deuterium found on Earth and in meteorites 
is about 1/10,000 of the abundance of hydrogen, and this may be 
the result of deuterium having been destroyed in the course of its 
period within the interiors of stars. In any case, the results seem to 
favour a model of a closed spherical universe, with the background 
radio noise originating from regions so far away that the symbolic 
velocities of recession amount to several thousands of millions of 
kilometres per second. 

The analysis of the colour/absolute magnitude diagram for 
globular clusters, taken together with the inner structures of the 
clusters themselves, ought to shed some light on the probable 
abundance of primitive helium at the time when the galaxies were 
formed. There is a good deal of uncertainty, because it looks as 
though different globulars have dillerent amounts of helium at the 



244 



present time, and some of thcni are helium-deficient. This sort of 
deficiency would favour open, hyperbolic models of the universe 
with a low density for the material, hut the destruction of primitive 
deuterium must also be borne in mind. 

To sum up: Either primitive helium was relatively scarce (with 
abundance about 10 per cent) and primitive deuterium has been 
burned up during the evolution of the stars in the galaxies, so that 
the evidence favours an open, hyperbolic model for the universe; 
or else primitive helium was abundant (around 30 per cent) and 
the present abundance of deuterium is the same as it has always 
been, in which case the universe is closed and spherical. 

Counting methods seemed formerly lo hold out hopes with 
regard lo the determination of cosmological models, but have 
proved lo be something of a disappointment, because we have no 
real idea of how the galaxies have developed o\er long periods of 
time. Analyses of radio sources also seemed promising, because 
the sources are powerful enough to be detected over greal distances, 
and yet quasar counts do not seem to fit in with any cosmological 
models so far proposed. It looks as though either the numbers of 
quasars evolve in time, or else the quasars themselves evolve with 
time. If so. quasars may provide vital clues to the overall processes 
of evolution. 

Systematic discussions of all homogeneous, uniform models of 
the universe have been completed by now, so lhat apart from the 
expansion parameter and the famous cosmological constant it 
ought to be possible lo work oul a parameter expressing rotation 
and also a parameter expressing the rate of deformation. In- 
vestigations of these various models, all of which are based on 
Einstein's general relativity, confirm thai the introduction of 
rotation or anisotropy raises difficulties when we come to consider 
expansion from a singular slate. Some authorities have questioned 
the reasons for such investigations: why. in fact, reject the idea of a 
singular stale, when the trouble may lie in the incompleteness of 
Einstein's equations? After all. the singular stale seems to be 
necessary in explaining the background radio radiation from ihe 



245 



sky. and it is worth noting lhat thirty years ago. Tolmann was 
speculating as to whether some relic of the universe could be found 
which would lake us back before the singular slate, to a time 
when contraction was still going on. 

Moreover, it is also possible lhat successive oscillations of the 
universe cause irreversible effects which accumulate - in which 
case the enlropy (i.e. the degree of molecular disorder in a system) 
of a closed spherical universe should increase steadily. Lively 
discussions about this point arc still going on, and are likely to 
continue for a long lime yet. 

Hoyle has now given up the idea of a steady-stale universe. If the 
theory had been correct, matter could never have passed through 
the physical state which seems necessary to explain the background 
radio emission, Hoyle has also underlined how his researches into 
general relativity had led him to attach importance to the terms 
which prevent the occurrence of a singular stale in the universe 
taken as a whole. 

We have seen above that quasars could be interpreted as pieces of 
matter erupting in our universe. Such views were originally due to 
Jordan and were taken up again more recently by Novikov and by 
Nceman. They should certainly be borne in mind, because it is 
possible with these theories to envisage the appearance of vast 
masses of matter undergoing differential expansion. Hoyle has 
attempted to explain the quasars in this way, mainly because of the 
extraordinary concentration of matter toward the centres of the 
systems. Authorities who follow more conventional ideas about the 
quasars are hardly likely lo accept new models of this sort. On the 
other hand, it is true that collisions between stars, with all the con- 
sequences arising, could lead to phenomena closely resembling the 
quasars, provided that the collisions are frequent enough: that is lo 
say. that the stars are sufficiently closely packed. It is not only 
direct collision that must be considered; wc must also remember 
that the stars will also cause intense friction against nebular matter, 
and coalescence might result in supernova explosions. The energy 
of the quasars might be explained in such ways, but it is not easy to 



246 



sec how any systems could have become dense enough for such 
remarkable interactions between stars to occur. 



6 Summary 



247 



It is now time to take stock of what has been said in this book. The 
universe observable from Earth is made up of stars and star- 
systems, with most systems including tremendous quantities of dust 
and gas. Our Galaxy is shaped like an immense disc, with a 
diameter of 100,000 light-years; the Sun lies some 30,000 light-years 
from the galactic nucleus, and completes one orbit in about 
250,000,000 years. There are about 100,000 million stars in the 
Galaxy; in the neighbourhood of the Sun there is an average of one 
star in a cube of side ten light-years, and when dust and gas are 
taken into consideration the average mass works out at two or 
three atoms of hydrogen per cubic centimetre. It is not possible to 
estimate the significance of the masses of obscure material, of 
slight mass, moving inside the Galaxy, but undoubtedly this 
material must exist. 

The chemical composition of the universe taken as a whole is 
uniform, but tremendous differences in detail are found in different 
regions, as has been found from studies of the composition of the 
Earth, the elements found in meteorites, and the relative abundances 
of the elements as estimated from the spectra of the stars. 

In our Galaxy there are many star-clusters, and for many of these 
reliable age-estimates can be made. Very young clusters appear to 
be several millions of years old. while others have ages of something 
of the order of 15,000 million years. Stars evolve over periods 
of lime, and their compositions are altered by nuclear transforma- 
tions; radioactive elements can be regenerated by the explosions of 
supernovse, and it may be that this process began with the forma- 
tion of our Galaxy 18,000 million years ago. 

Beyond our system there are other galaxies, of which one of the 
nearest is the Andromeda Spiral, at a distance of 2,200,000 light- 
years. They are of varied forms; elliptical, spiral and diffuse. There 
are radio galaxies, and also the quasars, often called quasi-stellar 
radio sources because they show up as starlike points when 
photographed. 

The galaxies evolve. Violent explosions give rise to radio 
emission, and some galaxies show traces of several successive 






248 



Bibliography 



249 



explosions. Systems of galaxies also evolve; there are multiple 
systems which seem to be only a few thousands of millions of 
years old. Quasars, a hundred times more luminous than the 
brightest elliptical galaxies, are energy sources of unparalleled 
violence, capable of releasing energy flux of the order of a million 
million times that of the Sun. Also, the galaxies are spread through- 
out space, and the brightest objects of all the quasars can be 
measured out to well over 6,000 million light-years. Euclidean 
geometry is no longer valid for such tremendous distances. The 
paths of light-rays are modified by the presence of matter., and this 
leads on to discussions of curved space, where properties analogous 
to those of two dimensions have to be adapted to a three-dimen- 
sional system. 

Consistent efforts are being made to decide whether the universe 
is open and hyperbolic, or closed and spherical. The Hubble- 
Humason relationship, and the background radio noise from the 
sky, seem to favour the spherical, closed model, but the matter is 
by no means settled. The density of material in the universe will be 
different for different models, but a mean density of 2 x 10" ^ does 
not seem to be incompatible with the best available spectroscopic 
results. Of course, there are other reasons for uncertainty as well. 
The expansion constant indicates an age for the universe of about 
10,000 million years, so that presumably some extraordinary 
event (the so-called 'big bang*) look place at that lime. And yet 
this seems to contradict the estimates for the ages of the oldest 
star-clusters in our Galaxy, so that much work remains to be done. 
A deeper study of the internal structures of the stars will give 
better values for the ages of the clusters, and these in turn will 
lead to better estimates for the age of the universe itself. 

As yet. nobody knows how these two theories can be reconciled. 






If a book has been published both in Britain and the United States both 
publishers are listed, die British one being named first. Dales are of first 
publication. 

Much of the material in this book is contained in recent issues of technical 
periodicals, such as the Astraphysical Journal, the Monthly Notices of the 
Royal Astronomical Society, the Astronomical Journal of the USSR and 
Annates D'Astmphysique. Handbooks containing knowledge at a fairly 
advanced technical standard include Stellar Structure, L.H.AUcr and D. B. 
MeLoughlin (eds). University of Chicago Press. London and Chicago. 1962 
(volume s ni li compendium of astronomy and astrophysics entitled Stars 
and Stellar Systems, under the general editorship of Gerard P. Kuiper and 
Barbara M.Middlehurst). 

The following semi-popular books will be found useful: 

Abell.G. (1964). Exploration of the Universe, Holt Rinchari and Winston. 

London and New York 
Abeili.G. and Hack.M. (1964). Nebulae and Galaxies. Fa ber.' Crowe 1 1 
Alfven.H. (1967). Worlds-Anthvorlds, Freeman, London 
Baade, W. ( 1963). The Evolution of Stars and Galaxies. Oxford U.P. "Harvard 

U.P. 
Bonnor.W.B. (1965). The Mystery of the Expanding Universe. Eyre and 

Spolliswoode/Macmillan 
Firsoft'.V.A. (1967). Facing the Universe. Sidgwtck and Jackson. London 
Hoyle.F. (1967). Galaxies. Nuclei and Quasars. Hdnemann/Harper 
Jennison.R.C. (1966). Introduction to Radio Astronomy, Newnes, London 
Kahn, l'.D, and Palmer. U.P. (1967). Quasars: their importance in astronomy 

and physics. Manchester U.P. /Harvard U.P. 
MeVittic.G.C. (1961). Fact and Theory in Cosmology, Eyre and Spottiswoode, 

Macmillan 
Moore, P. (1967), Astronomy, Oldbournc/Grosset and Diinlap 
Moore, P. (1967). The New Look of the Universe, Zenith/Norton 
North, J. D. (1965). The Measure of the Universe, Oxford U.P.. London and 

New York 
Schatzman, E. (1966). 77ie Origin and Evolution of the Universe, Hutchinson - 

Basic Books 
Shapley.B. (1961). Galaxies. Oxford U.P./Harvard U.P. 



Acknowledgments 



Index 



251 



Acknowledgment is due to the following for the photographs (the numbers 
refer to the pttge on which (he illustration appears). 

Frontispiece © 1965 California Institute of Technology and Carnegie 
Institute of Washington: 10 R.A.S.. W.Lockyer; 14,17,19,34-5,36,38-9,43. 
47,59,69,120-1,123.125 Patrick Moore; 22.26-7,125 Mount Wilson and 
Palomar Observatories; 49,60.130 R.A.S.; 113 R.A.S., R.O. Cape; 121 
Lick Observatory. 









Abcll.L. 177,183 
Acceleration 85 

cosmical 211 ct seq. 
AUvdn.H. 234 6 
A mba rts u m i an, V. 146,160,205 
Andromeda Galaxy 9, 1 1 . 12. 122, 1 24, 

128,147,154,155.246 
Angstrom unit 61 
Antimatter 234-6 
Atoms, structure of 89 90 
Atomic nuclei, composition of 88 
Atomic transitions 62 

BaadcW. 12 
Baum,W. 217 
Bessel.F.W. II 
Bondi.H. 18,225,231 
Burbidge.G. 20 
Burbidgc,M. 20 

Caesium clocks 89 

Carle thiCiel 29 

Ccphcids 11,12.13.44,46,120 

Clerk MaxwcII.J. 72 

Clusters, sec Star clusters 

Colour Index 52,110 

Coma cluster 1 52, 1 58, 1 59, 1 60. 1 79 

Continuous creation, see Steady Hate 

theory 
Copernicus 9,32 
Cosmic rays 68,72, 191-2 
Cosmical repulsion 210-1 
Cosmology 192 et seq. 

Einstein's 209-10 

fried ma mi's 210 

Newtonian 207-9 
Crab Nebula 67,78 
Curie, I. 103 
Curvature 193,200-1 

of space 206-7 

Day. length of 85 
deSitier.W. 16 



de Vaucoulcurs.G. 174 
Dicke's hypothesis 228,232 
Diffusion 70 
Dirac.P.A.M. 227,231 
Distances, cosmical 80 
Dopplcr EITect 40-2,130-2,151 

Earth, age of 91-2 
Eddmgion.A.S. 16 
Einstein, A, 12,16,222 
Electromagnetic spectrum 61 
Elements: origin of 20-1 

radioactive age of 92 4 

stable 107 
Elliptical galaxies 1 55, 157-8 
Ephemeris time 85 
Explorer IX 236 

Faraday rotation 77 
Fowler, W. 20 
Friedmann.A. 16,210 
Fl Orionis 116 

Galaxies: catalogue of (Shaplcy-Ames) 
169.174 

classification of 1 18, 132-6, 164 
clusters of 127 8, 157-9, 160, 169, 
176-7,179,181-3,237 
colliding, theory of 146 
elliptical, sec Elliptical galaxies 
evolution of 168 
grouping of 179,180-1 
masses of 146 9,151.157.159,160. 
165,168 

most luminous stars in 126-7 
multiple 139,145 7,160 
novue in 11,120,122 
numbers of 118,175-6,185,226. 
237-8 * 

radio 136-9 

recession and distance 12, 120 ct seq. 
spectral classification of 134-6 
status of 32 



252 



Galaxy, (he. age of 243 

centre of 58 

evolution or tOO. 1 1 5, 1 1 6 7 

gas and dust in 57 8,8 1,84 

magnetic field of 69.70.72,76-8; 

mass of 1 5 1 

radio emission from 61 

shape of 9,29,50,246 

status of 1 5 
Gauss, K. 201 
Galileo 85 
Geodesies 193 

Geometry on a surface 196-201 
Gold,T. 18,225.227,231 
Graphite, interstellar 74 
Gravitation 48-50, 147 

H-R diagrams 53,56-7 

Hen rich 20 

Herschel.W. 9 

Hcrusprung, E. S3 

Horizon, cosmic 223 

Hoyle.F, 18,20,225.231,233,239,245 

Hubble, E. 12, 13. 130. 132. 134-5. 164. 

175,182.185,247 
Hubble-Humason Law 12,151 
Humason.M. 12.130.169,217 
Hyades 44,52 
Hydra cluster 1 3 1 
Hydrogen clouds in Galaxy, the 62,64 

Inert ial mass 86 
Isochrones 99 
Isotopes 89 

Jolioi.F. 103 

Jordan's theory 205,228,231,245 

Kant.l. 9 

KirchholT, G. 42 
Koinomallcr 235 

Lambcrt.J. 15 



Langevin's paradox 220-1 
LcmaUre. Canon 16 
l.equeux.M. 129 
Luminosity function 128 

Mach.E. 16.222 

Magellanic Cloud, large 122 3,146 
Magellanic Cloud, small 44,122 3 
Magnitude, absolute 37 
Main Sequence 52,97 
Maupcrtuis, M.de 9 
Mayall,W. 13,20,169,217 
Magnelic fields 69,70,72 

interstellar 76-7 
Magnelic mirrors 70 
Messier, C. 9 
Milky Way. the 29.58 
Mineur.H. 13 

NarlikarJ.V. 234,239 

Nebulae 9.12,29,32,58 

Neeman 205,245 

Neumann 15 

Neutrinos 103-5,192 

Neutrons 103-4.106,109 

New General Catalogue (Dreyer ) II 

Newton, Isaac 48 

Novae in galaxies 1 1, 120, 122 

Novikov 205.245 

Nucleosynthesis 100 2 

Olbcrs" Paradox 186-9 
Oort.J.H. 185 

Pachncr's Theory 239-40 
Palo mar Sky Atlas 29 
Parallax, spectroscopic 57 

trigonometrical 32-3 
Parsec, the 77,120 
Poisson's Frequency 1 83 A 
Polarisation 72,81 

interstellar 74,81 
Populations, stellar 57,81, 117, 146, 152 



253 






Proxima Centauri 33,80 

Quasars 1 5,42, 1 36, 1 37 -8, 1 6 1 , 1 64. 204. 
2 ! 7, 2 1 9, 223, 227. 233, 240- 1 , 244. 
246-7 

RR Lyrac variables 44-5,46, 120, 122 
Radio radiation 61 2,64-5,67 
Radio sources 1 3, 67, 1 36-9, 1 89, 1 9 1 , 

244 
Radio telescopes 13 
Radio waves from space 13 

at 21 centimetres 62,154,242 
Radioactivity 89,90-1.239 

constant of 90 

time of 91 
Red Shifts of galaxies 130-2,188,224 

nature of 230 3,236 
Relativity 15,201-3 
Relaxation lime 156 
Riemannian geometry 24 1 
Ritchey.C. II 
Rockets 61 
Russell, H.N. 53 

Sandage.A. 13,169.217.219 

Schwarzschild.K. 18,204.209-10 

Schwa rzschild's singularity 203-5 

Scorpio, X-ray source in 67 

Sccligcr.H. 15 

Semenov.V, 235 

Shane, CD. 175 

Shapley.H. 169,174.177 

Singular stale 18,238-9 

Sinus 29 

Sliphcr.V. 128 

Spiral galaxies, form of 1 52-4 

Sun, in the Galaxy 48,53v81 

Star clusters, ages of 99. 100,229,236 

246,247 

globular 111-2,122 
Star-streaming 37.40 
Stars, ages of 18.94.97,99, 100, 1 12 



distances of 32 3 
distribution of. in the Galaxy 48 
encounters between 1 56- 7, 245 
energy source of 18.94,97 
evolution or 97.99, 112,229 
giant and dwarf 52-3,56-7 
high-velocity 50,112,115 
luminosities of 52-3, 56 
magnitudes of 23,29 
metal abundance in 1 12. 1 15, 1 17 
numbers of 29,81 
proper motions of 42-4 
radial motions of 42-4 
spectral types of 52-3 
variable 44,46 

Sicady-slalc theory 18,225-7,232-3 

Stcphan's Quinlct 147 

Supergalaxy, the 1 74-5 

Supemovuc 13.78. 102-3, 109, 1 16-7 

Synchrotron radiation 65,76 

Technetium 20 
Time: and the atom 89 

and energy 86-7 

and light 80-1,87,89 

cosmic 219 223 

mechanical 85,86 
Time-dilation effect 220- 1 

Universe, age of 18.242-3.247 
mean density of matter in 185-6, 
240.247 

non-unirorm (Tolmann) 21 
origin of 16,238,242 3 

Virial, the 155,160 

Weight mass 86 
Wrighl.T. 9 

X-rays 61,65,67,189 

Zwicky.F. 160,175,177,231.237 



World University Library 

Books published or in preparation 



255 



Economics and 
Social Studies 



The World Cities 

Peter Hall. London 

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Jagdish Bhagwati, MIT 

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Human Communication 
J. L. Aranguren, Madrid 

Education in the Modern World 
John Vaizey. London 

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Roger Opie. Oxford 

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Michael Kaset. Oxford 

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J. L. Sampedro, Madrid 

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Roger Hood, Durham 

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15001 700 

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Jurgen Kuczynsfci. Berlin 

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Robert North. Stanford 

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and Stress 

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EL. Schatzman, Pans 

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H.FIohn. Bonn 

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Andre Cailleux, Paris 



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Renty Chauvm. Strasbourg 

Primates 

Francois Bourhere. Paris 

The Age of the Dinosaurs 

8|orn Kurten. Helsinki 



Physical Science and 
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The Quest for Absolute Zero 

K. Mendelssohn. Oxford 
What is Light 7 
A. C S van Heel and 
C. H F. Velzel. Eindhoven 

Mathematics Observed 

Hans Freudenlhal. Utrecht 

Waves and Corpuscles 

J. L Andrade e Silva and G. Lochak. 
Paris Introduction by Louis de Broglie 



Applied Science 

Words and Waves 

AH W, Beck. Cambridge 

The Scienceof Decision making 
A. Kaulmann. Parts 

Bionics 

Lucien Gerard in. Parts 

Data Study 

J. L. Jolley, London 



E. L. Schatzman is Professor of 
Astrophysics in the Faculty of Sciences 
at Paris. 



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